埃尔米特-爱因斯坦流形的刚性结果

Mathematical Proceedings of the Royal Irish Academy Pub Date : 2013-11-25 DOI:10.3318/PRIA.2016.116.03

Stuart J. Hall, T. Murphy

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引用次数: 4

摘要

研究了A. Gray在K\ ahler-Einstein流形的单位球束上引入的微分算子。导出了K\ ahler-Einstein流形单位球束上Sasaki度规拉普拉斯算子第一特征值的下界。在此基础上，推导了复空间形式在紧密厄米曲面和所有K\ ahler-Einstein曲面中两条投影线积的刚性定理。

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Rigidity results for Hermitian-Einstein manifolds

A differential operator introduced by A. Gray on the unit sphere bundle of a K\"ahler-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 K\"ahler-Einstein manifold is derived. Some rigidity theorems classifying complex space forms amongst compact Hermitian surfaces and the product of two projective lines amongst all K\"ahler-Einstein surfaces are then derived.

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Mathematical Proceedings of the Royal Irish Academy

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