Rigidity results for Hermitian-Einstein manifolds

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 compl...

Full description

Saved in:
Bibliographic Details
Published inMathematical proceedings of the Royal Irish Academy Vol. 116A; no. 1; pp. 35 - 44
Main Authors S.J. Hall, T. Murphy
Format Journal Article
LanguageEnglish
Published Royal Irish Academy 2016
Subjects
Curvature
Differential operators
Eigenvalues
Laplacians
Mathematical constants
Mathematical manifolds
Mathematical surfaces
Mathematical theorems
Scalars
Tensors
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1393-7197
2009-0021
DOI:10.3318/PRIA.2016.116.03