Manwë and the other Valar are mentioned by Tolkien in his letter of Milton Waldman, letter 131 in Letters of J. R. R. Tolkien, Tolkien says, in part:
On the side of mere narrative device, this is, of course, meant to provide beings of the same order as the ‘gods’ of higher mythology, which can be accepted – well, shall we say baldly, by a mind that believes in the Blessed Trinity.
Tolkien never suggests that Eru is one of these Valar. Eru, their creator, is far above them. And not enough is told of Eru to suggest that any of Tolkien’s characters from creation to the early years of the Fourth Age ever imagined him in Triune Form.
Manwë is much more like the angel St. Michael in traditional Christian mythology, although I am unaware that anyone asked Tolkien whether they were supposed to be identical. In the Christian Biblical Book of Revelations, St. Michael Michael leads God’s armies against Satan's forces. During the war in heaven St. Michael defeats Satan.
St. Michael is also comparable with Tulkas who casts down Morgoth in the First War and with Eönwë who is leader of the host who captures Melkor at the end of the First Age.
Tolkien in his inventions largely avoids traditions that have become part of most forms of Christianity or Judaism. Tolkien provides no figure who must be St. Michael and no creation in six days followed by God resting on the seventh day. The seven-day Númenórian week is represented as in origin an adaptation of the six-day Eldarin week and, at least among the Hobbits the partial day of rest at the end of the week is equated with Friday, as in the Muslim calendar.
The Hindu Trinity is largely an intellectual construct to unify the separate cults of Vishnu and Shiva, adding Brahma the creator who seems to be a priestly idea, never much worshipped. In mythological tales Brahma is almost always subordinate to either Vishnu or Shiva. Some Hindus worship mainly Vishnu, mostly under his incarnation of Krishna, some worship mainly Shiva, and some worship mainly the goddess Durga or Kali. All these deities are normally recognized by all worshippers.
In Hindu religious thinking, Vishnu/Shiva would be identified with Eru and and the Valar with Indra and his circle of gods, these gods mostly being very seldom worshipped. But in the tales Indra is mostly much degraded and is forced to rely on Vishnu or Shiva when any crisis occurs in the heavens.