1. Geometric inequalities for CR-submanifolds
- Author
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Djorić, Mirjana and Rovenski, Vladimir
- Subjects
Mathematics - Differential Geometry - Abstract
We study two kinds of curvature invariants of Riemannian manifold equipped with a distribution (for example, a CR-submanifold of an almost Hermitian manifold) related to sets of pairwise orthogonal subspaces of the distribution: one is similar to Chen's $\delta$-invariants and another kind of invariants is based on the mutual curvature of the subspaces. We compare Chen-type invariants with the mutual curvature invariants and prove geometric inequalities with intermediate mean curvature squared for CR-submanifolds in almost Hermitian spaces. In the case of a set of complex planes, we study curvature invariants based on the concept of holomorphic bisectional curvature. As applications, we give consequences of the absence of some $D$-minimal CR-submanifolds in almost Hermitian manifolds., Comment: 8 pages
- Published
- 2024