Is Vishnu the incarnation of Krishna or the other way around, according to the Geetha?


"Which is true according to the holy books?"

Well, the answer is that both are true! :)

There are some verses in the scriptures which say that Krishna is incarnation of Vishnu, but there are also verses in the scriptures which say the other way round, namely that Vishnu is incarnation of Krishna. So both of those views are true. I don't see any good reason to believe that just one of those group of verses are true, while the other group of verses that tell the opposite is somehow untrue. Both must be true because that what scripture teaches is true!
So, sometimes when the Lord appears in this world as an avatara, specifically as Krishna, He is incarnation of Vishnu. But sometimes when the Lord appears in this world as an avatara Vishnu, He is incarnation of Krishna.

That what ISKCON devotees have taught you is correct. From the Bhagavad gita we only learn that Vishnu is incarnation of Krishna!, and there are no verses in the Gita that say Krishna is incarnation of Vishnu!

Here is what we learn from the Gita about who is whose incarnation, ie who is whose avatara:
There is a chapter in the Bhagavad gita titled vibhūti-yogaḥ "The Opulence of the Absolute", it's 10th chapter, see at
In that chapter Lord Krishna is talking about his own opulence or vibhūti. This is seen from the verses 18-19:

10.18 — O Janārdana, again please describe in detail the mystic power of Your opulences. I am never satiated in hearing about You, for the more I hear the more I want to taste the nectar of Your words.
10.19 — The Supreme Personality of Godhead said: Yes, I will tell you of My splendorous manifestations, but only of those which are prominent, O Arjuna, for My opulence is limitless.

But what is remarkable to note is the thing that in the following verses Lord Krishna not only mentions various things and living beings as manifestations of his opulence (vibhūti), but He also mentions several forms of Lord Vishnu, ie several well known incarnations (avataras) of Lord Vishnu, as his own opulence (vibhūti)!
Thus He clearly indicates that those forms of Lord Vishnu are, indeed, his incarnations (avataras)! Here are those verses:

10.21 — Of the Ādityas I am Viṣṇu
10.26 — ... among perfected beings I am the sage Kapila
10.29 — Of the many-hooded Nāgas I am Ananta
10.31 — ... of the wielders of weapons I am Rāma
10.37 — Of the descendants of Vṛṣṇi I am Vāsudeva

Thus those five incarnations (avataras) of Lord Vishnu, namely Vishnu Aditya, Kapila, Ananta, Rama (Ramachandra), and Vāsudeva (identified as Balarama), are manifestations of Lord Krishna's opulence (vibhūti), and thus they are Lord Krishna's incarnations (avataras). Here it's worth to mention that Vāsudeva referred to in verse 37 acaryas who commented upon the Bhagavad gita explained as Lord Krishna's brother Balarama.

This view about those five forms of Lord Vishnu who are enumerated as Lord Krishna's opulence being His avataras or incarnations is even further strengthened with a verse 41 in the same chapter where Lord Krishna says that all those vibhūti or opulences that He described are just an aṁśa "a part" of his splendor:

yad yad vibhūtimat ... mama tejo-’ṁśa-sambhavam

mama — My; tejaḥ — of the splendor; aṁśaa part

Know that all opulent, beautiful and glorious creations spring from but a spark of My splendor.

It is important to know here that word aṁśa is used throughout Vedic scriptures in the sense of "avatara", or "incarnation" in English. And thus as a matter of fact Lord Krishna is saying that those five Vishnu forms are his avataras or incarnations.

As far as I know there are no verses in the Bhagavad gita which say that Krishna is incarnation (avatara) of Vishnu, but there are only those verses which I explained above that say the other way round.

Note: I will update my post with additional explanation later when I find some time.

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