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

Abstract

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 Kähler 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).

16 pages

References in corpus (1)

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