Complex manifolds with split tangent bundle
代数几何
2007-05-23 v2
摘要
Let X be a compact Kaehler manifold. We expect that any direct sum decomposition of the tangent bundle T(X) comes from a splitting of the universal covering space of X as a product of manifolds, in such a way that the given decomposition of T(X) lifts to the canonical decomposition of the tangent bundle of a product. We prove this assertion when X is a Kaehler-Einstein manifold or a Kaehler surface. Simple examples show that the Kaehler hypothesis is necessary.
引用
@article{arxiv.math/9809033,
title = {Complex manifolds with split tangent bundle},
author = {Arnaud Beauville},
journal= {arXiv preprint arXiv:math/9809033},
year = {2007}
}
备注
9 pages, Plain TeX. We give a simpler proof of Theorem A following a paper of Yau