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Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.

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Conceptual understanding of the definition for Hermite-Einstein metrics

I'm studying holomorphic vector bundles $(E,h)$ on Kähler manifolds that admit a Hermite-Einstein metrics. Particularly, I'm trying to find the motivation for the definition. An hermitian structure $ …
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