Soft Restrictions on Positively Curved Riemannian Submersions

被引：6

作者：

Gonzalez-Alvaro, David ^{[1
,2
]}

Guijarro, Luis ^{[1
,2
]}

机构：

[1] Univ Autonoma Madrid, Dept Math, Madrid, Spain

[2] ICMAT CSIC UAM UCM UC3M, Madrid, Spain

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2016年 / 26卷 / 02期

关键词：

Riemannian submersions; Positive sectional curvature; Wilking's transverse equation; NONNEGATIVE CURVATURE; CONJUGATE-POINTS; GEODESICS; FOLIATIONS;

D O I：

10.1007/s12220-015-9596-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We bound the dimension of the fiber of a Riemannian submersion from a positively curved manifold in terms of the dimension of the base of the submersion and either its conjugate radius or the length of its shortest closed geodesic.

引用

页码：1442 / 1452

页数：11

共 14 条

[1]

Amman M., ARXIV14031440

[2]

[Anonymous], 1996, TRANSLATIONS MATH MO

[3] SOME EXISTENCE THEOREMS FOR CLOSED GEODESICS [J].

BALLMANN, W ;

THORBERGSSON, G ;

ZILLER, W .

COMMENTARII MATHEMATICI HELVETICI, 1983, 58 (03) :416-432

[4]

Fet A. I., 1951, DOKL AKAD NAUK SSSR, V81, P17

[5]

Gromoll D., 2009, Progress in Mathematics, V268

[6] CONJUGATE-POINTS ON SPACELIKE GEODESICS OR PSEUDO-SELF-ADJOINT MORSE-STURM-LIOUVILLE SYSTEMS [J].

HELFER, AD .

PACIFIC JOURNAL OF MATHEMATICS, 1994, 164 (02) :321-350

[7]

Jimenez W., 2006, THESIS

[8] RIEMANNIAN FOLIATIONS ON MANIFOLDS WITH NONNEGATIVE CURVATURE [J].

KIM, H ;

TONDEUR, P .

MANUSCRIPTA MATHEMATICA, 1992, 74 (01) :39-45

[9] Notes on the Jacobi equation [J].

Lytchak, Alexander .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2009, 27 (02) :329-334

[10] SUBMERSIONS AND GEODESICS [J].

ONEILL, B .

DUKE MATHEMATICAL JOURNAL, 1967, 34 (02) :363-&

← 1 2 →