Scalar curvature rigidity of almost Hermitian spin manifolds which are asymptotically complex hyperbolic

Mario Listing

Scalar curvature rigidity of almost Hermitian spin manifolds which are asymptotically complex hyperbolic

Differential Geometry 2007-05-23 v2

Authors: Mario Listing

Abstract

This paper generalizes a rigidity result of complex hyperbolic spaces by M. Herzlich. We prove that an almost Hermitian spin manifold $(M,g)$ of real dimension $4n+2$ which is strongly asymptotic to $\hyp{\C}^{2n+1}$ and satisfies a certain scalar curvature bound must be isometric to the complex hyperbolic space. The fact that we do not assume $g$ to be K\"ahler reflects in the inequality for the scalar curvature.

Keywords

scalar curvature rigidity almost hermitian spin manifolds complex hyperbolic asymptotically complex hyperbolic

Cite

@article{arxiv.math/0402142,
  title  = {Scalar curvature rigidity of almost Hermitian spin manifolds which are asymptotically complex hyperbolic},
  author = {Mario Listing},
  journal= {arXiv preprint arXiv:math/0402142},
  year   = {2007}
}

Comments

8 pages. submitted to Comm. Anal. Geom

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