Curvature of the second kind and a conjecture of Nishikawa
Curvature of the second kind and a conjecture of Nishikawa
In this paper we investigate manifolds for which the curvature operator of the second kind (following the terminology of Nishikawa (1986)) satisfies certain positivity conditions. Our main result settles Nishikawaā€™s conjecture that a manifold with positive curvature operator of the second kind is diffeomorphic to a sphere, by showing that ā€¦