On a generalized conjecture of Hopf with symmetry

Manuel Amann; Lee Kennard

doi:10.1112/S0010437X16008150

On a generalized conjecture of Hopf with symmetry

Manuel Amann, Lee Kennard

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

5 Scopus citations

Abstract

A famous conjecture of Hopf states that does not admit a Riemannian metric with positive sectional curvature. In this article, we prove that no manifold product can carry a metric of positive sectional curvature admitting a certain degree of torus symmetry.

Original language	English (US)
Pages (from-to)	313-322
Number of pages	10
Journal	Compositio Mathematica
Volume	153
Issue number	2
DOIs	https://doi.org/10.1112/S0010437X16008150
State	Published - Feb 1 2017
Externally published	Yes

Keywords

Euler characteristic
Hopf conjecture
positive curvature
torus symmetry

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X16008150

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title = "On a generalized conjecture of Hopf with symmetry",

abstract = "A famous conjecture of Hopf states that does not admit a Riemannian metric with positive sectional curvature. In this article, we prove that no manifold product can carry a metric of positive sectional curvature admitting a certain degree of torus symmetry.",

keywords = "Euler characteristic, Hopf conjecture, positive curvature, torus symmetry",

author = "Manuel Amann and Lee Kennard",

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AU - Kennard, Lee

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KW - Euler characteristic

KW - Hopf conjecture

KW - positive curvature

KW - torus symmetry

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On a generalized conjecture of Hopf with symmetry

Abstract

Keywords

ASJC Scopus subject areas

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