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

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

2004-08-06

arxiv.org/abs/math/0408092v1

Mathematics

Differential Geometry

16 pages

Scientific paper

We show that an almost Hermitian manifold $(M,g)$ of real dimension $4n$ which is strongly asymptotic to $\mathbb{C}H^{2n}$ and satisfies a certain scalar curvature bound must be isometric to the complex hyperbolic space. Assuming K\"ahler instead of almost Hermitian this gives the already known rigidity result by H. Boualem and M. Herlich proved in \emph{Ann. Scuola Norm. Sup Pisa (Ser. V)}, vol. 1(2).

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