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

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  • Thierno Seck
  • Athoumane Niang
  • Antonio Masiello

Abstract

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.

Suggested Citation

  • Thierno Seck & Athoumane Niang & Antonio Masiello, 2022. "Conformal Metrics to a Product or Doubly Warped Product on S2×S2 and the Hopf Conjecture," Journal of Mathematics, Hindawi, vol. 2022, pages 1-5, June.
    • Handle: RePEc:hin:jjmath:6268017
    DOI: 10.1155/2022/6268017
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