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On complete manifolds of nonnegative $ k$th-Ricci curvature

Author: Zhong Min Shen
Journal: Trans. Amer. Math. Soc. 338 (1993), 289-310
MSC: Primary 53C21; Secondary 31C12, 57R70
MathSciNet review: 1112548
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Abstract: In this paper we establish some vanishing and finiteness theorems for the topological type of complete open riemannian manifolds under certain positivity conditions for curvature. Key tools are comparison techniques and Morse Theory of Busemann and distance functions.

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