Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture

Hopf’s well-known conjecture states that there exists no metric of positive sectional curvature in the product manifold S2×S2. In this paper, we show that the Hopf conjecture is true for conformal metrics to the product metric or doubly warped products on S2×S2.

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Bibliographic Details
Main Authors: Thierno Seck, Athoumane Niang
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/6268017
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author Thierno Seck
Athoumane Niang
author_facet Thierno Seck
Athoumane Niang
author_sort Thierno Seck
collection DOAJ
description Hopf’s well-known conjecture states that there exists no metric of positive sectional curvature in the product manifold S2×S2. In this paper, we show that the Hopf conjecture is true for conformal metrics to the product metric or doubly warped products on S2×S2.
format Article
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institution OA Journals
issn 2314-4785
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-20a0f2cb2d804c5b83010575cb34eaaa2025-08-20T02:03:58ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6268017Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf ConjectureThierno Seck0Athoumane Niang1Département de Mathématiques et InformatiqueDépartement de Mathématiques et InformatiqueHopf’s well-known conjecture states that there exists no metric of positive sectional curvature in the product manifold S2×S2. In this paper, we show that the Hopf conjecture is true for conformal metrics to the product metric or doubly warped products on S2×S2.http://dx.doi.org/10.1155/2022/6268017
spellingShingle Thierno Seck
Athoumane Niang
Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture
Journal of Mathematics
title Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture
title_full Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture
title_fullStr Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture
title_full_unstemmed Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture
title_short Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture
title_sort conformal metrics to a product or doubly warped product on s2 s2 and the hopf conjecture
url http://dx.doi.org/10.1155/2022/6268017
work_keys_str_mv AT thiernoseck conformalmetricstoaproductordoublywarpedproductons2s2andthehopfconjecture
AT athoumaneniang conformalmetricstoaproductordoublywarpedproductons2s2andthehopfconjecture