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

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.