Einstein–Hermitian vector bundle (Q5349809)
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a Hermitian holomorphic vector bundle over a Kähler manifold, whose Chern connection’s curvature satisfies Einstein’s equations (i.e. equals the identity times a constant)
- Hermitian Yang-Mills bundle
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Einstein–Hermitian vector bundle |
a Hermitian holomorphic vector bundle over a Kähler manifold, whose Chern connection’s curvature satisfies Einstein’s equations (i.e. equals the identity times a constant) |
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Statements
![{\displaystyle {\begin{aligned}(E,\nabla _{E}^{\text{Chern}})&\twoheadrightarrow (M,g_{i{\bar {\jmath }}})\\R_{i{\bar {\jmath }}}[\nabla _{E}^{\text{Chern}}]&=\Lambda g_{i{\bar {\jmath }}}\operatorname {id} _{E}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e081f5d630b396a903ce6ed27eed5a118ecb89f1)
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