Let $E\to X$ be a Hermitian holomorphic vector bundle over a Kahler manifold and denote by $Y$ the total space of $E$ as a complex manifold. What would be the connection (and curvature) of $Y$ in terms of the connections (and curvatures) of $X$ and $E$?
2026-04-08 05:50:40.1775627440
Curvature of the total space of a vector bundle
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