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

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

2004-02-09

arxiv.org/abs/math/0402142v2

Mathematics

Differential Geometry

8 pages. submitted to Comm. Anal. Geom

Scientific paper

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.

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