Connectedness at infinity of complete Kähler manifolds and locally symmetric spaces

2007/01/30 by Li, Peter, Wang, Jiaping
#58J90 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0701865

Abstract

One of the main purposes of this paper is to prove that on a complete Kähler manifold of dimension m, if the holomorphic bisectional curvature is bounded from below by -1 and the minimum spectrum λ₁(M) ≥ m², then it must either be connected at infinity or diffeomorphic to \Bbb R × 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 Kähler manifolds satisfying a weighted Poincaré inequality are also being considered

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