Structures on manifolds | Riemannian geometry | Complex manifolds

Hermitian connection

In mathematics, a Hermitian connection is a connection on a Hermitian vector bundle over a smooth manifold which is compatible with the Hermitian metric on , meaning that for all smooth vector fields and all smooth sections of . If is a complex manifold, and the Hermitian vector bundle on is equipped with a holomorphic structure, then there is a unique Hermitian connection whose (0, 1)-part coincides with the Dolbeault operator on associated to the holomorphic structure.This is called the Chern connection on . The curvature of the Chern connection is a (1, 1)-form. For details, see Hermitian metrics on a holomorphic vector bundle. In particular, if the base manifold is Kähler and the vector bundle is its tangent bundle, then the Chern connection coincides with the Levi-Civita connection of the associated Riemannian metric. (Wikipedia).

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Hermitian Operators (Self-Adjoint Operators) | Quantum Mechanics

In this video, we will talk about Hermitian operators in quantum mechanics. If an operator A is a Hermitian operator, then it is the same as its adjoint operator A-dagger, which is defined via this equation here. Usually, the terms "Hermitian" and "self adjoint" are used interchangeably, h

From playlist Quantum Mechanics, Quantum Field Theory

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From playlist Differential Equations with YouTube Examples

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From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020

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From playlist THE "WHAT IS" PLAYLIST

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From playlist Research Lectures

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From playlist Higgs Bundles

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From playlist QED- Prerequisite Topics

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From playlist Non-Hermitian Physics (ONLINE)

Related pages

Holomorphic vector bundle | Levi-Civita connection | Complex manifold