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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A bridge between complex geometry and Riemannian geometry


Author: Antonio Cassa
Journal: Proc. Amer. Math. Soc. 119 (1993), 621-628
MSC: Primary 53C56; Secondary 32C10
MathSciNet review: 1152272
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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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DOI: https://doi.org/10.1090/S0002-9939-1993-1152272-2
Article copyright: © Copyright 1993 American Mathematical Society