Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Geometry, topology > Topology ( the situation in geometry ) > Analytic topology > Flow -shaped geometry

Some Results on Curvature and Topology of Open Manifold

Author LuWen
Tutor LiGongBao
School Central China Normal University
Course Basic mathematics
Keywords large volume growth finite topological type diffeomophic
CLC O189.31
Type Master's thesis
Year 2007
Downloads 9
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In this paper, we study the noncompact manifold by virtue of comparison, more precisely, conditions on curvature are given to ensure the noncompact manifold being diffeomorphic to Rn. As we know, the study of noncompact manifolds turns more complicated than the compact ones,whose attributes guarantee simpler calculations and estimates.Here as follows are our main results.1. Let (M,g)be a complete n-manifold satisfyingSuppose thatthen (M,g) has finite topology type.2. Given positive numbersα> 0, r0 > 0 and an integer n≥2, there is an∈=∈(n,α,r0) > 0, such that any complete Riemannian n-manifold M,with Ricci curvature RicM≥0,αm≥α, Kpmin≥-1, cp≥r0 andfor some p∈Mand allr≥r0 is diffeomorphic to Rn.3. Givenα∈((1/2),1)and an integer n≥2,there is constant r0 = r0(α,n),∈=∈(n,α)> 0, such that any complete Riemannian n-manifold M, with RicM≥0,αM≥α,KMmin≥-1 andfor some p∈M and all r≥r0 is diffeomorphic to Rn. 4. Let M be a complete n-manifold, KMmin≥0 ifthen M is diffeomorphic to Rn.

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