The Partial Ricci Flow for Foliations

Abstract

We introduce and study new structures, which generalize the 3-(quasi-)Sasakian structure, an f -structure with parallelizable kernel, and an almost para-φ-structure with complemented frames (having constant partial Ricci curvature) and are of particular interest in the study of the partial Ricci flow of metrics on a totally geodesic foliation. We show convergence of the partial Ricci flow on a g-foliation with any of our novel structures.

New integral formulae for two complementary orthogonal distributions on Riemannian manifolds

“…2, Eq. (4)] and has been applied by several authors in different contexts (see [5,7,14,17,18] etc.). Recently, first Rovenski and the second author [15] on symmetric spaces and then Andrzejewski [2] (see also [3]) on arbitrary Riemannian manifolds have found series of integral formulae for codimension-one foliations, formulae which extend (1) and all the equalities proved in [4] and [6].…”