Complex manifolds with split tangent bundle

Arnaud Beauville

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arXiv · math/9809033

Complex manifolds with split tangent bundle

Arnaud Beauville

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Abstract

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.

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BibTeX RIS

Arnaud Beauville. 1998-10-09. Complex manifolds with split tangent bundle. https://arxiv.org/abs/math/9809033

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