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.

On the completeness of total spaces of horizontally conformal submersions

In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.

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.

New types of almost contact metric submersions

We introduce the concept of conjugaison in contact geometry. This concept allows to define new structures which are used as base space of a Riemannian submersion. With these new structures, we study new three types of almost contact metric submersions.

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.

Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces

We show that every 3-$$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifold of dimension $$4n + 3$$ 4 n + 3 admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature $$16n(n+2)\alpha \delta$$ 16 n ( n + 2 ) α δ . In the non-degenerate case we describe all homogeneous 3-$$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifolds fibering over symmetric Wolf spaces and over their non-compact dual symmetric spaces. If $$\alpha \delta > 0$$ α δ > 0 , this yields a complete classification of homogeneous 3-$$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifolds. For $$\alpha \delta < 0$$ α δ < 0 , we provide a general construction of homogeneous 3-$$(\alpha , \delta )$$ ( α , δ ) -Sasaki manifolds fibering over non-symmetric Alekseevsky spaces, the lowest possible dimension of such a manifold being 19.

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.

On the Geometry of Submersions

Subject of present paper is the geometry of foliation defined by submersions on complete Riemannian manifold. It is proven foliation defined by Riemannian submersion on the complete manifold of zero sectional curvature is total geodesic foliation with isometric leaves. Also it is shown level surfaces of metric function are conformally equivalent.

Semi-invariant Riemannian submersions from nearly Kaehler manifolds

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.