Yes, there is, but you need to understand both contextual concepts to the word Logos in Christianity and its equivalency in Hinduism. In the Christian Bible it states - "In the beginning was the Word, and the Word was with God, and the Word was God" The 'Word' being 'Logos'. The first concept is that the Logos and God were One before creation and the Word was the first manifestation of God, and the personification of God is the Word. The first manifestation of God in creation was the Word, and Jesus is the Word and Jesus is the incarnation (avatar) of God. Jesus and God are One.
The first concept, that the Word was the first manifestation of God, is in Hinduism. Swami Vivekananda writes (Complete Works, Vol 3, section Bhakti Yoga, subsection The Mantra: OM: Word and Wisdom; available here - https://advaitaashrama.org/cw/content.php):
In the universe, Brahmâ or Hiranyagarbha or the cosmic Mahat first manifested himself as name, and then as form, i.e. as this universe. All this expressed sensible universe is the form, behind which stands the eternal inexpressible Sphota, the manifester as Logos or Word. This eternal Sphota, the essential eternal material of all ideas or names is the power through which the Lord creates the universe: nay, the Lord first becomes conditioned as the Sphota, and then evolves Himself out as the yet more concrete sensible universe. This Sphota has one word as its only possible symbol, and this is the (Om). And as by no possible means of analysis can we separate the word from the idea, this Om and the eternal Sphota are inseparable; and therefore, it is out of this holiest of all holy words, the mother of all names and forms, the eternal Om, that the whole universe may be supposed to have been created. But it may be said that, although thought and word are inseparable, yet as there may be various word-symbols for the same thought, it is not necessary that this particular word Om should be the word representative of the thought, out of which the universe has become manifested. To this objection we reply that this Om is the only possible symbol which covers the whole ground, and there is none other like it. The Sphota is the material of all words, yet it is not any definite word in its fully formed state. That is to say, if all the peculiarities which distinguish one word from another be removed, then what remains will be the Sphota; therefore this Sphota is called the Nâda-Brahma. the Sound-Brahman.
Now, as every word-symbol, intended to express the inexpressible Sphota, will so particularise it that it will no longer be the Sphota, that symbol which particularises it the least and at the same time most approximately expresses its nature, will be the truest symbol thereof; and this is the Om, and the Om only; because these three letters (A.U.M.), pronounced in combination as Om, may well be the generalised symbol of all possible sounds. The letter A is the least differentiated of all sounds, therefore Krishna says in the Gita — "I am A among the letters". Again, all articulate sounds are produced in the space within the mouth beginning with the root of the tongue and ending in the lips — the throat sound is A, and M is the last lip sound, and the U exactly represents the rolling forward of the impulse which begins at the root of the tongue till it ends in the lips. If properly pronounced, this Om will represent the whole phenomenon of sound-production, and no other word can do this; and this, therefore, is the fittest symbol of the Sphota, which is the real meaning of the Om. And as the symbol can never be separated from the thing signified, the Om and the Sphota are one. And as the Sphota, being the finer side of the manifested universe, is nearer to God and is indeed that first manifestation of divine wisdom this Om is truly symbolic of God. Again, just as the "One only" Brahman, the Akhanda-Sachchidânanda, the undivided Existence-Knowledge-Bliss, can be conceived by imperfect human souls only from particular standpoints and associated with particular qualities, so this universe, His body, has also to be thought of along the line of the thinker's mind.
In Hinduism, therefore, the Sphota, OM, is the equivalent of the Logos. The Aitreya Upnaishad I.i.1 (Swami Nikhilananda translator) says:
In the beginning [all] this verily was Atman only, one and without a second. There was nothing else that winked. He bethought Himself: "Let Me now create the worlds."
The other concept that Logos identifies with is the personification of the Godhead through an incarnation. Christian theology says there has only been one incarnation- Jesus. Hinduism, on the other hand, says that there have been several incarnations, and will be in the future. Krishna says in the Gita, Chapter 4 verses 7-8 (Swami Nikhilananda translator):
Whenever there is a decline of dharma, O Bharata, and a rise of adharma, I incarnate Myself.
For the protection of the good, for the destruction of the wicked, and for the establishment of dharma, I am born in every age.
Guy L. Beck says:
Most scholars of Hinduism and Indian history accept the historicity of Krishna – that he was a real male person, whether human or divine, who lived on Indian soil by at least 1000 BCE and interacted with many other historical persons within the cycles of the epic and puranic histories.
— (Alternative Krishna, Suny press, pg 4–5)
Horace H. Wilson said:
Rama and Krishna, who appear to have been originally real and historical characters…
— (The Visnu Purana. Nag Publishers. 1989, pg. ii)
Dr. Thomas J. Hopkins, 1978:
From a strictly scholarly, historical standpoint, the Krishna who appears in the Bhagavad-Gita is the princely Krishna of the Mahabharata... Krishna, the historical prince and charioteer of Arjuna.
— (Five Distinguished Scholars on the Krishna movement in the West. Groves Press, N.Y. l983, pg. 144.)
Rudolf Otto opined:
That Krishna himself was a historical figure is indeed quite indubitable.
— (The Original Gita, cit. for Majumdar Bimanbihari, ot. cit. pg. 5)
The New British Encyclopaedia:
Vasudeva-Krisna, a historical Vrisni prince who was presumably also a religious leader levitated to the Godhead by the 5th century BC.
— (The New Encyclopaedia Britannica, 1984, vol. 7 Micropedia, pg.7)
Dr. R. C. Majumdar:
There is now a general consensus of opinion in favour of the historicity of Krishna. Many also hold the view that Vâsudeva the Yadava hero, the cowherd boy Krishna in Gokula… were one and the same person.
— (The History and Culture of the Indian people, vol. I, pg. 303)
Dr. Bimanbihari Majumdar, 1968:
The western scholars at first treated Krishna as a myth... But many of the Orientalists in the present century have arrived at the conclusion that Krishna was a historical ksatriya warrior who fought at Kuruksetra,... .
The answer to that will differ from sect to sect. To many Vaishnava Hindus (those seeing Vishnu as the ultimate God) Krishna is the ultimate God. Even amount Vaishnavas this isn't universal, others see Narayan as the ultimate Got and Krishna as an avatar.
Some Advaita sects see the ultimate God as the pervasive formless and impersonal Bramin and all forms of God as just higher level illusions. (I am not clear on the impersonal bit, if an Advaita sees this maybe they can clarify. Some seem to describe it as hyper-personal having all possible attributes of person simultaneously and just as all colours simultaneously appear white to our limited perception this appears to us as blank and impersonal)
According to the Vedas and the Upanishads, said to have originated as far back as the 3rd millennium BCE, then handed down from generation to generation and formulated into a philosophical system by Hindu mystics during the first millennium CE, the human soul, Atman, is one with the Brahman, which is Ultimate Reality. The Creator of the cosmos, the Brahma, is actually a secondary deity. We live, unavoidably, in the Samsara, the phenomenal world of objects of our perception, which is constantly changing. We achieve liberation (Moksha) from the phenomenal world through the endless cycle of death and rebirth, on the basis of the principle of Karma, whereby the human soul faces (or enjoys) the consequences of its actions, both in this life and in their next rebirth. But the Ultimate Reality is one with the human soul, it is not a transcendent being to which each individual is subject. In present-day eastern (and in some western) philosophy we find many variations on this same theme: there is no Ultimate Reality, or God, which or who is external to human Self. The Self is represented as consubstantial with the Divine. Every human soul is his or her own divine reality. This conception of reality is known as monism and elements of it have permeated many different philosophical traditions for millennia.
As regards Western philosophy, and specifically Greek philosophy, the names that most readily spring to mind are Socrates, Plato and Aristotle. But these philosophers countered, or developed and refined ideas that preceded them. As in the case of the oriental traditions, the definition of Ultimate Reality and humankind’s relation to it was of utmost importance to these Greek philosophers. The preceding “mythological” age had been characterised by a pantheon of competing deities, who were larger than life versions of human heroes, with their very human foibles and phobias. It was the philosophers, probably starting with Thales (600 BCE), not the poets, who began to grapple with the true nature of the realities that shaped human behaviour, and they mocked the simplistic beliefs that were enshrined in the works of Homer and others. But that did not mean that these philosophers were atheists. Xenophanes, for example, who poured scorn on “the gods” and those who believed in them, nevertheless sounds like a monotheist when he said, “One god, greatest among gods and men, in no way similar to mortals in body or in thought.” And “Always he remains in the same place, moving not at all; nor is it fitting for him to go to different places at different times, but without toil he controls all things by the thought of his mind”. This will remind us of the concept of the “unmoved mover” later developed by Aristotle.
When Thales said, “everything is full of gods” he was not referring to transcendent beings worthy of worship and reverence. He meant something like the forces that made people and matter behave in one way or another. Matter preceded the “gods”, not vice versa. At the most, “the gods” shaped and imposed order on the stuff that the universe was made of. Even when they seemed inclined towards monotheism, for the Greeks God did not create the cosmos. The very term cosmos refers to the order which this creative force (god) imposed on the original chaos. This creator did not originate the system whereby chaos and cosmos are kept in tension, he/it is part of it. The universe is an emanation from god, and is therefore part of god, and vice versa. In a sense, everything is God. God is somehow the energy that inhabits the universe, moving and directing it to optimal effect.
But what did the stuff of the universe consist of? What was the primal substance of which it was made, the arche as they called it? For Thales this primal substance was water, while for Anaximander it was what he called apeiron, that is a substance without boundaries or limits. This limitless, infinite substance held opposite qualities in tension, in a state of equilibrium. The earth itself is held in place by being equidistant from everything surrounding it. Anaximenes held that everything had its origin in air. Heraclitus, for his part, argued that everything is in a state of flux, which is the theory that is most often associated with him. However, he also deserves to be credited with originating the concept of logos, the basic principle that held all the fluctuating phenomena together.
John begins with a statement these philosophers could affirm (“in the beginning was the Logos“), another that some might accept (“the Word was with God”), and a third that all would have questioned (“the Word was God”). He stakes out his ground right from the beginning — for John, the Logos is a Person, and not just any Person, but God Himself, distinct (and so with God) yet also God. The Tri-Unity of God is in view here, for verse one is meaningless unless there is both a diversity and a unity within God. But John’s focus is not so much on the Triune nature of God as it is on the Person he is calling the Word. He rejects from the beginning the idea of logos as an impersonal force or principle in nature.1 In the beginning was the Word, and the Word was with God, and the Word was God.
2 The same was in the beginning with God.
The philosophers saw the logos as the pattern or principle underlying nature. Here, it is as if John says, “Close, but not really. He is more than just the pattern, He is the active mover in creation. He made everything.”All things were made by him; and without him was not any thing made that was made.
The philosophers may have seen the logos as the generative principle behind all of matter and nature, but John says, “No, Jesus is the One who is truly Life, the Life and the Light of men.”In him was life; and the life was the light of men.
Heraclitus had said that people did not understand and live by the logos. In this verse, it is almost as if John says to Heraclitus, “Yes, you are right, and you do not comprehend the Logos, either. For He is light and you are in darkness.”And the light shineth in darkness; and the darkness comprehended it not.
The Logos was made FleshTo this point, the humanistic philosophers of John’s day might have found this an interesting discussion. They were always looking to hear some new thing (Acts 17:21), new gods and ideas, and this could have sounded like some expansion of Heraclitus’ old logos philosophy. To talk about the Logos as a deity who came but was received by few (John 1:10-12) would have been an interesting philosophical idea to many of them.
But now, John wrote words completely alien to the pagan philosophers:
Not only was the Logos a divine Person, He was also Man. He was made flesh, human, and lived among men. The pagans had stories about gods living among men, but not about them actually becoming human. And yet, that is what John said — He became flesh, fully human. Yet, He was still fully divine, the only begotten (see my article from earlier this month on this). Though John was again using the term Logos in this verse, he was unfolding truths completely beyond the conception of any pagan philosopher.And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
There are three main differing philosophies on Hinduism. The first is Advaita Vedanta that believes that Brahman and Atman are identical. The second is Dvaita Vedanta which sees them as forever separate but of the same or similar nature, most schools of this philosophy believe that souls were not created but always existed. The third Vishishtadvaita sees souls as a part of Brahman but separate, each person having a unique divine spark.The Self is represented as consubstantial with the Divine. Every human soul is his or her own divine reality. This conception of reality is known as monism and elements of it have permeated many different philosophical traditions for millennia.
Ancient Greek philosophers believed in a similar idea of an impersonal God like entity.
A lot of people who are brought up in proscriptive religions don't see this at first. Asking "What do Hindus believe about Krishna" is not like asking "What do Christians believe about Jesus?". It is much more akin to asking "What do Abrahamic religions believe about Jesus?" if Abrahamic religions were treated as one religion and Christianity, Judaism, Islam, Druze, Rastafarianism, and maybe secular humanism, etc seen as sects or lineages. One "Abrahamic" would say "He is God", another would say "He was a profit", and another "He was just one of many preachers at the time", and all would be quite happy for others to believe differently.Yes. So what is it you are asking? Krishna is different things in different traditions.