Scalar and φ-Sectional Curvature of a Certain Type of Metric f-Structures

Abstract

We consider a Riemannian manifold (M, g) equipped with an fstructure of constant rank with parallelizable kernel. We assume certain integrability conditions on such a manifold. We prove some inequalities involving the scalar and * -scalar curvature of g. We prove that the corresponding equalities characterize an S-manifold, which is a generalization of a Sasakian manifold. We also give a method of constructing such structures on toroidal bundles. Mathematics Subject Classification (2000). Primary 53D10; Secondary 70G45.

The Partial Ricci Flow for Foliations

“…If we take a higher dimensional abelian Lie algebra, then as examples of such g-manifolds can serve K, S or C manifolds, e.g., cf. [10,9]. 3-Sasakian manifolds, cf.…”