Contact-Complex Riemannian Submersions

A submersion from an almost contact Riemannian manifold to an almost Hermitian manifold, acting on the horizontal distribution by preserving both the metric and the structure, is, roughly speaking a contact-complex Riemannian submersion. This paper deals mainly with a contact-complex Riemannian submersion from an η-Ricci soliton; it studies when the base manifold is Einstein on one side and when the fibres are η-Einstein submanifolds on the other side. Some results concerning the potential are also obtained here.

Riemannian submersions for q-entropies

In an attempt to find the dynamical foundations for [Formula: see text]-entropies, we examine the special case of Lagrangian/Hamiltonian systems of many degrees of freedom whose statistical behavior is conjecturally described by the [Formula: see text]-entropic functionals. We follow the spirit of the canonical ensemble approach. We consider the system under study as embedded in a far larger total system. We explore some of the consequences that such an embedding has, if it is modeled by a Riemannian submersion. We point out the significance in such a description of the finite-dimensional Bakry–Émery Ricci tensor, as a local mesoscopic invariant, for understanding the collective dynamical behavior of systems described by the [Formula: see text]-entropies.

Anti-invariant Riemannian submersions from Sasakian manifolds with totally umbilical fibers

The purpose of this paper is to study anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds such that characteristic vector field is vertical or horizontal vector field. We first show that any anti-invariant Riemannian submersions from Sasakian manifold is not a Riemannian submersion with totally umbilical fiber. Then we introduce anti-invariant Riemannian submersions from Sasakian manifolds with totally contact umbilical fibers. We investigate the totally contact geodesicity of fibers of such submersions. Moreover, under this condition, we investigate Ricci curvature of anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds.

Spectral Estimates for Riemannian Submersions with Fibers of Basic Mean Curvature

For Riemannian submersions with fibers of basic mean curvature, we compare the spectrum of the total space with the spectrum of a Schrödinger operator on the base manifold. Exploiting this concept, we study submersions arising from actions of Lie groups. In this context, we extend the state-of-the-art results on the bottom of the spectrum under Riemannian coverings. As an application, we compute the bottom of the spectrum and the Cheeger constant of connected, amenable Lie groups.

Triharmonic Riemannian submersions from 3-dimensional space forms

We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.