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

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

2008-02-18

arxiv.org/abs/0802.2474v1

Mathematics

Differential Geometry

4 pages, no figure

Scientific paper

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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