My question is how do the Mahayana sutras describe the behavioral characteristics of a realized bodhisattva? How does he behave? For example an Arahant is described as having “characteristics that please the noble ones”. Or something like that. Is there something similar in mahayana Buddhist sutras?
From Vimalakirti Sutra:
At that time, there lived in the great city of Vaisali a certain Licchavi, Vimalakirti by name. Having served the ancient Buddhas, he had generated the roots of virtue by honoring them and making offerings to them. He had attained tolerance as well as eloquence. He played with the great superknowledges. He had attained the power of incantations and the fearlessnesses. He had conquered all demons and opponents. He had penetrated the profound way of the Dharma. He was liberated through the transcendence of wisdom. Having integrated his realization with skill in liberative technique, he was expert in knowing the thoughts and actions of living beings. Knowing the strength or weakness of their faculties, and being gifted with unrivaled eloquence, he taught the Dharma appropriately to each. Having applied himself energetically to the Mahayana, he understood it and accomplished his tasks with great finesse. He lived with the deportment of a Buddha, and his superior intelligence was as wide as an ocean. He was praised, honored, and commended by all the Buddhas and was respected by Indra, Brahma, and all the Lokapalas. In order to develop living beings with his skill in liberative technique, he lived in the great city of Vaisali.
His wealth was inexhaustible for the purpose of sustaining the poor and the helpless. He observed a pure morality in order to protect the immoral. He maintained tolerance and self-control in order to reconcile beings who were angry, cruel, violent, and brutal. He blazed with energy in order to inspire people who were lazy. He maintained concentration, mindfulness, and meditation in order to sustain the mentally troubled. He attained decisive wisdom in order to sustain the foolish.
He wore the white clothes of the layman, yet lived impeccably like a religious devotee. He lived at home, but remained aloof from the realm of desire, the realm of pure matter, and the immaterial realm. He had a son, a wife, and female attendants, yet always maintained continence. He appeared to be surrounded by servants, yet lived in solitude. He appeared to be adorned with ornaments, yet always was endowed with the auspicious signs and marks. He seemed to eat and drink, yet always took nourishment from the taste of meditation. He made his appearance at the fields of sports and in the casinos, but his aim was always to mature those people who were attached to games and gambling. He visited the fashionable heterodox teachers, yet always kept unswerving loyalty to the Buddha. He understood the mundane and transcendental sciences and esoteric practices, yet always took pleasure in the delights of the Dharma. He mixed in all crowds, yet was respected as foremost of all.
In order to be in harmony with people, he associated with elders, with those of middle age, and with the young, yet always spoke in harmony with the Dharma. He engaged in all sorts of businesses, yet had no interest in profit or possessions. To train living beings, he would appear at crossroads and on street corners, and to protect them he participated in government. To turn people away from the Hinayana and to engage them in the Mahayana, he appeared among listeners and teachers of the Dharma. To develop children, he visited all the schools. To demonstrate the evils of desire, he even entered the brothels. To establish drunkards in correct mindfulness, he entered all the cabarets.
He was honored as the businessman among businessmen because he demonstrated the priority of the Dharma. He was honored as the landlord among landlords because he renounced the aggressiveness of ownership. He was honored as the warrior among warriors because he cultivated endurance, determination, and fortitude. He was honored as the aristocrat among aristocrats because he suppressed pride, vanity, and arrogance. He was honored as the official among officials because he regulated the functions of government according to the Dharma. He was honored as the prince of princes because he reversed their attachment to royal pleasures and sovereign power. He was honored as a eunuch in the royal harem because he taught the young ladies according to the Dharma.
He was compatible with ordinary people because he appreciated the excellence of ordinary merits. He was honored as the Indra among Indras because he showed them the temporality of their lordship. He was honored as the Brahma among Brahmas because he showed them the special excellence of gnosis. He was honored as the Lokapala among Lokapalas because he fostered the development of all living beings.
Thus lived the Licchavi Vimalakirti in the great city of Vaisali, endowed with an infinite knowledge of skill in liberative techniques.
If you want to know all about realized Bodhisattvas, their way of life and what their minds are like, you can do no better than Shantideva's Guide to the Bodhisattva's Way of Life.
Picture the most sublimely altruistic mind(s) imaginable without one bit of self-cherishing and devoted only to that which is beneficial for other sentient beings in a completely equaniminous and unbiased manner. Beings who have completely devoted all their countless future lives to practicing Dharma solely for the benefit of others.
For me, this quote from that work captures the feeling best and provides a vivid description of what the mind of a realized Bodhisattva must be like:
“For as long as space endures
And for as long as living beings remain,
Until then may I too abide
To dispel the misery in the world.”
Imagine truly embodying that sentiment in every action of body, speech, and mind that one undertakes. For me, it is incredibly beautiful and awe inspiring.