A remark on the Herzlich volume of asymptotically complex hyperbolic Einstein manifolds

2008/02/18 by Yann Rollin, Rollin, Yann
Mathematics · #32Q20 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:32Q20 #msc:53C25

paper · pdf · doi:10.48550/arxiv.0802.2474

4 pages, no figure

arxiv created 2008/02/18 · openalex publication_date 2008/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We observe inequalities involving the Herzlich volume of a 4-dimensional asymptotically complex hyperbolic Einstein manifold and its Euler characteristic provided the metrics is either Kaehler or selfdual. In the selfdual case we have to assume furthermore that the Kronheimer-Mrowka invariant is non vanishing.

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