On a generalized conjecture of Hopf with symmetry

Manuel Amann, Lee Kennard

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)313-322
Number of pages10
JournalCompositio Mathematica
Volume153
Issue number2
DOIs
StatePublished - Feb 1 2017
Externally publishedYes

Fingerprint

Positive Curvature
Sectional Curvature
Symmetry
Riemannian Metric
Torus
Metric

Keywords

  • Euler characteristic
  • Hopf conjecture
  • positive curvature
  • torus symmetry

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On a generalized conjecture of Hopf with symmetry. / Amann, Manuel; Kennard, Lee.

In: Compositio Mathematica, Vol. 153, No. 2, 01.02.2017, p. 313-322.

Research output: Contribution to journalArticle

Amann, Manuel ; Kennard, Lee. / On a generalized conjecture of Hopf with symmetry. In: Compositio Mathematica. 2017 ; Vol. 153, No. 2. pp. 313-322.
@article{60630845c476419d81f1b66382e2c7fb,
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",
year = "2017",
month = "2",
day = "1",
doi = "10.1112/S0010437X16008150",
language = "English (US)",
volume = "153",
pages = "313--322",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - On a generalized conjecture of Hopf with symmetry

AU - Amann, Manuel

AU - Kennard, Lee

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Euler characteristic

KW - Hopf conjecture

KW - positive curvature

KW - torus symmetry

UR - http://www.scopus.com/inward/record.url?scp=85030447824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030447824&partnerID=8YFLogxK

U2 - 10.1112/S0010437X16008150

DO - 10.1112/S0010437X16008150

M3 - Article

AN - SCOPUS:85030447824

VL - 153

SP - 313

EP - 322

JO - Compositio Mathematica

JF - Compositio Mathematica

SN - 0010-437X

IS - 2

ER -