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

8 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

Access to Document

10.1007/s00039-007-0625-8

Cite this

@article{6f0a80f1a17e43259d1ae4f32092d57f,

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",

month = nov,

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

language = "English",

volume = "17",

pages = "1237--1247",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Topology of complete manifolds with radial curvature bounded from below

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

UR - http://www.scopus.com/inward/record.url?scp=38849111911&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38849111911&partnerID=8YFLogxK

U2 - 10.1007/s00039-007-0625-8

DO - 10.1007/s00039-007-0625-8

M3 - Article

AN - SCOPUS:38849111911

VL - 17

SP - 1237

EP - 1247

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 4

ER -

Topology of complete manifolds with radial curvature bounded from below

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this