A bridge between complex geometry and Riemannian geometry

Cassa, Antonio

doi:10.1090/S0002-9939-1993-1152272-2

A bridge between complex geometry and Riemannian geometry
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Proc. Amer. Math. Soc. 119 (1993), 621-628 Request permission

Abstract:

Every complex manifold ${M^n}$ with holomorphic metric can be obtained (at least locally) from a complex manifold ${E^{2 \bullet n - 2}}$ and one of its $\mathbb {C}$principal bundles $L$. The manifold $E$ is made of all (signed) complex geodesies of $M$ and $L$ is the bundle on $E$ of all choices of "times" evolving along the geodesies.

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