Topology of complete manifolds with radial curvature bounded from below

Kei Kondo; Shin Ichi Ohta

doi:10.1007/s00039-007-0625-8

Topology of complete manifolds with radial curvature bounded from below

Kei Kondo, Shin Ichi Ohta

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We investigate the topology of a complete Riemannian manifold whose radial curvature at the base point is bounded from below by that of a von Mangoldt surface of revolution. Sphere theorem is generalized to a wide class of metrics, and it is proven that such a manifold of a noncompact type has finitely many ends.

Original language	English
Pages (from-to)	1237-1247
Number of pages	11
Journal	Geometric and Functional Analysis
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/s00039-007-0625-8
Publication status	Published - Nov 2007
Externally published	Yes

Keywords

Number of ends
Radial curvature
Radius sphere theorem
Riemannian manifold
Von Mangoldt surface of revolution

ASJC Scopus subject areas

Analysis
Geometry and Topology

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title = "Topology of complete manifolds with radial curvature bounded from below",

abstract = "We investigate the topology of a complete Riemannian manifold whose radial curvature at the base point is bounded from below by that of a von Mangoldt surface of revolution. Sphere theorem is generalized to a wide class of metrics, and it is proven that such a manifold of a noncompact type has finitely many ends.",

keywords = "Number of ends, Radial curvature, Radius sphere theorem, Riemannian manifold, Von Mangoldt surface of revolution",

author = "Kei Kondo and Ohta, {Shin Ichi}",

note = "Funding Information: Keywords and phrases: Riemannian manifold, radial curvature, von Mangoldt surface of revolution, radius sphere theorem, number of ends AMS Mathematics Subject Classification: 53C20, 53C21 The second author was partially supported by the Grant-in-Aid for Scientific Research for Young Scientists (B) 16740034 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.",

year = "2007",

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doi = "10.1007/s00039-007-0625-8",

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AU - Kondo, Kei

AU - Ohta, Shin Ichi

N1 - Funding Information: Keywords and phrases: Riemannian manifold, radial curvature, von Mangoldt surface of revolution, radius sphere theorem, number of ends AMS Mathematics Subject Classification: 53C20, 53C21 The second author was partially supported by the Grant-in-Aid for Scientific Research for Young Scientists (B) 16740034 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

PY - 2007/11

Y1 - 2007/11

N2 - We investigate the topology of a complete Riemannian manifold whose radial curvature at the base point is bounded from below by that of a von Mangoldt surface of revolution. Sphere theorem is generalized to a wide class of metrics, and it is proven that such a manifold of a noncompact type has finitely many ends.

AB - We investigate the topology of a complete Riemannian manifold whose radial curvature at the base point is bounded from below by that of a von Mangoldt surface of revolution. Sphere theorem is generalized to a wide class of metrics, and it is proven that such a manifold of a noncompact type has finitely many ends.

KW - Number of ends

KW - Radial curvature

KW - Radius sphere theorem

KW - Riemannian manifold

KW - Von Mangoldt surface of revolution

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SN - 1016-443X

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ER -

Topology of complete manifolds with radial curvature bounded from below

Abstract

Keywords

ASJC Scopus subject areas

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