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arXiv · 1311.6279

Rigidity Results for Hermitian-Einstein manifolds

Stuart James Hall·Thomas Murphy
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Abstract

A differential operator introduced by A. Gray on the unit sphere bundle of a Kähler-Einstein manifold is studied. A lower bound for the first eigenvalue of the Laplacian for the Sasaki metric on the unit sphere bundle of a Kähler-Einstein manifold is derived. Some rigidity theorems classifying complex space forms amongst compact Hermitian surfaces and the product of two projective lines amongst all Kähler-Einstein surfaces are then derived.

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Stuart James Hall, Thomas Murphy. 2015-12-29. Rigidity Results for Hermitian-Einstein manifolds. https://arxiv.org/abs/1311.6279

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