Connectedness at infinity of complete Kähler manifolds and locally symmetric spaces

Details Connectedness at infinity of complete Kähler manifolds and locally symmetric spaces Connectedness at infinity of complete Kähler manifolds and locally symmetric spaces

2007-01-30

arxiv.org/abs/math/0701865v2

Mathematics

Differential Geometry

Scientific paper

One of the main purposes of this paper is to prove that on a complete K\"ahler manifold of dimension $m$, if the holomorphic bisectional curvature is bounded from below by -1 and the minimum spectrum $\lambda_1(M) \ge m^2$, then it must either be connected at infinity or diffeomorphic to $\Bbb R \times N$, where $N$ is a compact quotient of the Heisenberg group. Similar type results are also proven for irreducible, locally symmetric spaces of noncompact type. Generalizations to complete K\"ahler manifolds satisfying a weighted Poincar\'e inequality are also being considered

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