Rigidity Results for Hermitian-Einstein manifolds
Differential Geometry
2015-12-31 v4
Abstract
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.
Cite
@article{arxiv.1311.6279,
title = {Rigidity Results for Hermitian-Einstein manifolds},
author = {Stuart James Hall and Thomas Murphy},
journal= {arXiv preprint arXiv:1311.6279},
year = {2015}
}
Comments
V4. Some typos corrected. To appear in Math. Proc. Roy. Irish. Acad