As Hinduism was a prominent religion of the Buddha's time (though not in today's unified form ), Buddha must have learnt about the Gita and krishna's philosophy. In fact, the Buddha's karma philosophy and the notion of 'skillful karma' ( performing actions as duty without getting attached to it) seem to be too close to Krishna's karma yoga philosophy to find any difference.
Is there any reference to the Gita or Krishna in Buddhist texts?
The dates given in Wikipedia's Bhagavad Gita article, for example,
Professor Jeaneane Fowler, in her commentary on the Gita, considers second century BCE to be the likely date of composition.
... and,
The so-called "Hindu Synthesis" emerged during the early Classical period (200 BCE - 300 CE) of Hinduism.[21][7][22] According to Alf Hiltebeitel, a period of consolidation in the development of Hinduism took place between the time of the late Vedic Upanishad (ca. 500 BCE) and the period of the rise of the Guptas (ca. 320–467 CE) which he calls the "Hindu Synthesis", "Brahmanic Synthesis", or "Orthodox Synthesis".[21] It developed in interaction with other religions and peoples:
The emerging self-definitions of Hinduism were forged in the context of continuous interaction with heterodox religions (Buddhists, Jains, Ajivikas) throughout this whole period, and with foreign people (Yavanas, or Greeks; Sakas, or Scythians; Pahlavas, or Parthians; and Kusanas, or Kushans) from the third phase on [between the Mauryan empire and the rise of the Guptas].
... and in Wikipedia's Krishna article,
Worship of the deity Krishna, either in the form of deity Krishna or in the form of Vasudeva, Bala Krishna or Gopala can be traced to as early as the 4th century BC.
... compared with the dates in the Gautama Buddha article,
The times of Gautama's birth and death are uncertain. Most historians in the early 20th century dated his lifetime as circa 563 BCE to 483 BCE.
... suggest to me it's possible that maybe the Buddha lived a little bit earlier (e.g. 100 years or more) than when Krishna became famous and when the Gita was composed.
If it's true that the Gita was written during a "synthesis" which occurred as a reaction to competition from Buddhism and Jainism and so on, that could explain why there's no commentary from the Buddha (i.e. that he lived slightly before then, and so any commentary would be anachronistic).
There are Buddhist suttas which recount the Buddha's talking with brahmins.
In summary the first sentence of the OP (i.e. "As Hinduism was a prominent religion of the Buddha's time (though not in today's unified form), Buddha must have learnt about the Gita and krishna's philosophy.") might be a slightly incorrect assumption.
In fact, the Buddha's karma philosophy and the notion of 'skillful karma' ( performing actions as duty without getting attached to it) seem to be too close to Krishna's karma yoga philosophy to find any difference.
The Buddhist skillful Karma is not to do any action as a duty without attachment but to perform action with volitions which contain the roots of non aversion, non craving and non ignorance.
In Buddhis volition is the forerunner of Karma. If the volition is good, i.e., roots of non aversion, non craving and non ignorance, then the results would be also good.
Is there any reference to the Gita or Krishna in Buddhist texts?
I don't think there are.
OP: Is there any reference to the Gita or Krishna in Buddhist texts?
No. Only the three Vedas (presumably Rg, Yajur and Sama Veda) are mentioned in Buddhist texts (see MN 95). No other Hindu texts are mentioned.
OP: In fact, the Buddha's karma philosophy and the notion of 'skillful karma' ( performing actions as duty without getting attached to it) seem to be too close to Krishna's karma yoga philosophy to find any difference.
TL;DR:
Actually, the two are very different.
Krishna taught to perform your duty and do not be attached to the fruit of actions. So, if your duty is as a warrior, then you should fight the battle but not be attached to the fruit of actions i.e. victory or loss.
The Buddha taught that intention (or volition) is the most important element of karma. It's impossible to fight in battle without having one's intention or volition tainted with aversion and delusion. Please see this answer.
Detailed quotes:
What did Lord Krishna teach?
From Bhagavad Gita 2.31-38:
Besides, considering your duty as a warrior, you should not waver. Indeed, for a warrior, there is no better engagement than fighting for upholding of righteousness. O Parth, happy are the warriors to whom such opportunities to defend righteousness come unsought, opening for them the stairway to the celestial abodes. If, however, you refuse to fight this righteous war, abandoning your social duty and reputation, you will certainly incur sin. People will speak of you as a coward and a deserter. For a respectable person, infamy is worse than death. The great generals who hold you in high esteem will think that you fled from the battlefield out of fear, and thus will lose their respect for you. Your enemies will defame and humiliate you with unkind words, disparaging your might. Alas, what could be more painful than that? If you fight, you will either be slain on the battlefield and go to the celestial abodes, or you will gain victory and enjoy the kingdom on earth. Therefore arise with determination, O son of Kunti, and be prepared to fight. Fight for the sake of duty, treating alike happiness and distress, loss and gain, victory and defeat. Fulfilling your responsibility in this way, you will never incur sin.
And what did the Buddha teach?
From Yodhajiva Sutta (SN 42.3):
Then Yodhajiva the headman went to the Blessed One and, on arrival, having bowed down to him, sat to one side. As he was sitting there he said to the Blessed One: "Lord, I have heard that it has been passed down by the ancient teaching lineage of warriors that 'When a warrior strives & exerts himself in battle, if others then strike him down & slay him while he is striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the company of devas slain in battle.' What does the Blessed One have to say about that?"
"Enough, headman, put that aside. Don't ask me that."
A second time... A third time Yodhajiva the headman said: "Lord, I have heard that it has been passed down by the ancient teaching lineage of warriors that 'When a warrior strives & exerts himself in battle, if others then strike him down & slay him while he is striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the company of devas slain in battle.' What does the Blessed One have to say about that?"
"Apparently, headman, I haven't been able to get past you by saying, 'Enough, headman, put that aside. Don't ask me that.' So I will simply answer you. When a warrior strives & exerts himself in battle, his mind is already seized, debased, & misdirected by the thought: 'May these beings be struck down or slaughtered or annihilated or destroyed. May they not exist.' If others then strike him down & slay him while he is thus striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the hell called the realm of those slain in battle. But if he holds such a view as this: 'When a warrior strives & exerts himself in battle, if others then strike him down & slay him while he is striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the company of devas slain in battle,' that is his wrong view. Now, there are two destinations for a person with wrong view, I tell you: either hell or the animal womb."
When this was said, Yodhajiva the headman sobbed & burst into tears. [The Blessed One said:] "That is what I couldn't get past you by saying, 'Enough, headman, put that aside. Don't ask me that.'"
"I'm not crying, lord, because of what the Blessed One said to me, but simply because I have been deceived, cheated, & fooled for a long time by that ancient teaching lineage of warriors who said: 'When a warrior strives & exerts himself in battle, if others then strike him down & slay him while he is striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the company of devas slain in battle.'
"Magnificent, lord! Magnificent! Just as if he were to place upright what was overturned, to reveal what was hidden, to show the way to one who was lost, or to carry a lamp into the dark so that those with eyes could see forms, in the same way has the Blessed One — through many lines of reasoning — made the Dhamma clear. I go to the Blessed One for refuge, to the Dhamma, and to the Community of monks. May the Blessed One remember me as a lay follower who has gone to him for refuge, from this day forward, for life."
there is this sutta...
the footnote says:
The "Dark One" or Kanha (Sanskrit: Krishna), is another name for Mara. He is the Indian Cupid (Kamadeva) and personifies sensual passions
Also in this sutta it says:
