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

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 Kähler reflects in the inequality for the scalar curvature.

8 pages. submitted to Comm. Anal. Geom

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• Scalar curvature rigidity of almost Hermitian manifolds which are asymptotic to $\mathbb{C}{H}^{2n}$