arXiv research

Study of contact-complex Riemannian submersions in various manifold classes.

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian ma…

Study of Yamabe solitons on specific geometric manifolds.

We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian man…

Study on Yamabe solitons on specific complex manifolds, focusing on torse-forming vector fields.

New solitons defined for Sasaki-like almost contact complex Riemannian manifolds.

We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, anti-invariant para-quaternion Riemannian submersions, and anti-invariant octonian Riemannian submersions. This…

Study on solitons in complex Riemannian manifolds with specific properties.

Study on Riemannian submersions from nearly Kaehler manifolds.

In this paper, we study biharmonic Riemannian submersions. We first derive bitension field of a general Riemannian submersion, we then use it to obtain biharmonic equations for Riemannian submersions with $1$-dimensional fibers and Riemannian submersions with basic mean curvature vector fields of fibers. These are used…

Bi-slant submersion generalizes slant and semi-slant submersion.

Study of harmonic Riemannian submersions from 3D geometries.

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesi…

We introduce slant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of slant Riemannian submersions defined on Sasakian manifolds. We also give an example of such slant submersions.

The paper studies a new submersion type with specific conditions.

We introduce anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on Sasakian manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and ha…

The aim of the present paper to define and study semi-slant $ξ^\perp-$Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of anti-invariant $ξ^\perp-$Riemannian submersions, semi-invariant $ξ^\perp-$Riemannian submersions and slant Riemannian submersions. We obtain characterizat…

In this paper, we study Riemannian submersions whose total manifolds admitting a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we st…

B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant Riemannian submersion) to the case of locally conformal Kaehl…

The paper establishes new Casorati inequalities for various Riemannian maps and submersions.

Study on $η$-Ricci-Yamabe solitons on Riemannian submersions.

Establish generalized Chen inequalities for Riemannian submersions and Riemannian maps with applications.

The paper derives curvature inequalities for submersions from quaternionic space forms.

The paper defines and explores Clairaut conformal submersions in Riemannian geometry.

This paper generalizes biharmonic Riemannian submersions to higher dimensions.

The paper classifies harmonic and biharmonic submersions from Sol space.

We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and find necessary-sufficient conditions for total manifold to be locally product Riemann…

The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant…

Paper classifies fibers of fat Riemannian submersions with non-negative curvature.

In this paper we introduce slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We obtain some results on slant Riemannian submersions of a cosymplectic manifolds. We also give examples and inequalities between the scalar curvature and squared mean curvature of fibres of such slant submer…

Survey on biharmonic Riemannian submersions, a dual concept of biharmonic submanifolds.

We introduce the notions of h-conformal slant submersions and almost h-conformal slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions, h-slant submersions, almost h-slant submersion a…

Study shows discrete spectra on base spaces for certain Riemannian submersions.

Generalizes O'Neill's equations to pseudo-Finsler submersions.

Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.

As a generalization of Riemannian submersions, horizontally conformal submersions, semi-invariant submersions, h-semi-invariant submersions, almost h-semi-invariant submersions, conformal semi-invariant submersions, we introduce h-conformal semi-invariant submersions and almost h-conformal semi-invariant submersions fr…

The paper classifies biharmonic immersions and submersions in specific spheres.

Study on geometric properties of h-conformal semi-invariant submersions.

The paper derives inequalities for Riemannian submersions and their applications.

Study variations of Riemannian submersions to maintain geodesic fibers and positive curvatures.

We introduce slant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a slant s…

Riemannian submersions can preserve positive intermediate Ricci curvature, but not necessarily.

The paper sets new bounds for Ricci-curvature in submersions and maps.

The paper derives inequalities for Riemannian submersions and applies them to specific space forms.

Study on spectral properties of Riemannian submersions with special fibers.

If $π:M\rightarrow B$ is a Riemannian Submersion and $M$ has positive sectional curvature, O'Neill's Horizontal Curvature Equation shows that $B$ must also have positive curvature. We show there are Riemannian submersions from compact manifolds with positive Ricci curvature to manifolds that have small neighborhoods of…

New submersion proves complex-valued harmonic map existence.