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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6268017 |
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| _version_ | 1850230166933995520 |
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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 |
| id | doaj-art-20a0f2cb2d804c5b83010575cb34eaaa |
| 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 |