Connectedness at Infinity of Complete Kähler Manifolds and Locally Symmetric Spaces
نویسندگان
چکیده
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) ≥ m, then it must either be connected at infinity or diffeomorphic to 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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