arXiv research

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

The paper proves a stronger Petersen--Wilhelm conjecture for principal bundles.

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

New rigidity result for fat bundles with equal vertical curvatures.

Paper studies equatorial concentration of measure in sphere immersions and submersions.

Let $π{:}\,(M,\mathcal{H})\to (B,b)$ be a submersion equipped with a horizontal connection $\cal H$ over a Riemannian manifold $(B,b)$. We present an intrinsic curvature condition that only depends on the pair $(\cal H,b)$. By studying a set of relative flat planes, we prove that a certain class of pairs $(\cal H,b)$ a…

Alan Weinstein showed that certain characteristic numbers of any Riemannian submersion with totally geodesic fibers and positive vertizontal curvatures are nonzero. In this paper we explicitly compute these invariants in terms of Chern and Pontrjagin numbers of the bundle. This allows us to show that many bundles do no…

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

Generalizes warped product submersion to conformal case.

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…

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

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…

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…

Constructs fat, shellable 3-spheres with specific $f$-vectors.

Paper introduces fat CW complexes including all closed manifolds.

The paper studies a new submersion type with specific conditions.

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…

Study on Riemannian submersions from nearly Kaehler manifolds.

Introduces fat Lie theory for Lie groupoids and algebroids.

Study anti-invariant submersions from holomorphic statistical manifolds.

Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant s…

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a conformal submersion and show that there are certain product …

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

Study of harmonic Riemannian submersions from 3D geometries.

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…

Akyol, M. A and Şahin, B. [Conformal semi-invariant submersions, Commun. Contemp. Math. 19, 1650011 (2017).] introduced the notion of conformal semi-invariant submersions from almost Hermitian manifolds. The present paper deal with the study of conformal generic submersions from almost Hermitian manifolds which extends…

Study of almost Yamabe solitons on Kaehler submersions.

The paper characterizes Clairaut conformal submersions on Ricci solitons.

The article proves the existence of horizontal immersions into fat distributions and contact structures.

The paper classifies harmonic and biharmonic submersions from Sol space.

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…

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…

Study Clairaut anti-invariant submersions on nearly Kaehler manifolds.

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 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…

Sharp inequalities and solitons studied in statistical submersions.

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

We introduce bi-slant $ξ^{\perp}$-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of slant and semi-slant $ξ^{\perp}$-Riemannian submersion. We give an example and investigate the geometry foliations. After we obtain necessary and sufficient conditions related to totally geo…

Study cohomology classes related to harmonic maps on submersions.

As a generalization of anti-invariant $ξ^\perp-$Riemannian submersions, we introduce conformal anti-invariant $ξ^\perp-$submersions from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of foliations which are arisen from the definition of a conformal submersion and find necessary …

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

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…

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…

Derives criteria for Kähler structures on holomorphic submersions.

A classic problem in physics is the origin of fat tailed distributions generated by complex systems. We study the distributions of stock returns measured over different time lags $τ.$ We find that destroying all correlations without changing the $τ= 1$ d distribution, by shuffling the order of the daily returns, causes…

This work is devoted to new constructions of symplectically fat fiber bundles. The latter are constructed in two ways: using the Kirwan map and expressing the fatness condition in terms of the isotropy representation related to the G-structure over some homogeneous spaces.

A $3$-dimensional Riemannian manifold is called Killing submersion if it admits a Riemannian submersion over a surface such that its fibers are the trajectories of a complete unit Killing vector field. In this paper, we give a characterization of proper biharmonic CMC surfaces in a Killing submersion. In the last part,…

Godin introduced the categories of open closed fat graphs $Fat^{oc}$ and admissible fat graphs $Fat^{ad}$ as models of the mapping class group of open closed cobordism. We use the contractibility of the arc complex to give a new proof of Godin's result that $Fat^{ad}$ is a model of the mapping class group of open-close…