WebHe called R˚ the curvature operator of the second kind, to distinguish it from the curvature operator Rˆ, which he called the curvature operator of the first kind. It was … Web1 de jan. de 2014 · In a Riemannian manifold, the Riemannian curvature tensor \(R\) defines two kinds of curvature operators: the operator \(\mathop {R}\limits ^{\circ }\) of first kind, acting on 2-forms, and the operator \(\mathop {R}\limits ^{\circ }\) of second kind, acting on symmetric 2-tensors. In our paper we analyze the Sinyukov equations of …

PRODUCT MANIFOLDS AND THE CURVATURE OPERATOR OF THE SECOND KIND

Webcurvature operator of the second kind for any α>n−2 n (see [11, Example 2.5]). In a subsequent work [12], the author proves that a closed Kähler surface with six-positive … WebUniversity of Oregon. The second author would like to thank the host researcher of her Post Doctoral fellowship in Japan, Prof. Dr. N. Sakamoto, for his kind help and amiable encouragement. 2 The skew symmetric curvature operator Let Gr J (V) be the Grassmannian of oriented 2-planes on V. Let 7r 6 Gr £ (V) be an oriented 2-plane. shannex ancaster

Product manifolds and the curvature operator of the second kind

Web7 de set. de 2024 · In 1986, Nishikawa [] conjectured that a closed Riemannian manifold with positive (respectively, nonnegative) curvature operator of the second kind is … Web30 de mar. de 2024 · This article aims to investigate the curvature operator of the second kind on Kähler manifolds. The first result states that an m-dimensional Kähler manifold … Web15 de dez. de 2024 · The second one states that a closed Riemannian manifold with three-nonnegative curvature operator of the second kind is either diffeomorphic to a spherical space form, or flat, or isometric to a quotient of a compact irreducible symmetric space. This settles the nonnegativity part of Nishikawa's conjecture under a weaker assumption. shannex amherst