arXiv research

Study of harmonic Riemannian submersions from 3D geometries.

Study cohomology classes related to harmonic maps on submersions.

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

The paper classifies harmonic and biharmonic submersions from Sol space.

New submersion proves complex-valued harmonic map existence.

Study on Riemannian submersions from nearly Kaehler manifolds.

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…

The paper studies a new submersion type with specific conditions.

This paper generalizes biharmonic Riemannian submersions to higher dimensions.

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

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

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 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 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…

As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions of slant Riemannian maps and investigate harmonicity of such maps. We also obtai…

As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: t…

The paper explores conformal submersions from Ricci solitons to Riemannian manifolds.

The paper classifies biharmonic immersions and submersions in specific spheres.

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book by Baird and Wood for details)…

For biharmonic maps, there is a famous conjecture named Chen's conjecture. In later paper, Wang and Ou gave an affirmative partial answer to submersion version of Chen's conjecture. In this paper, we give an affirmative partial answer to submersion version of generalized Chen's conjecture, that is, triharmonic Riemanni…

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 …

Study cohomology classes related to $n$-harmonic morphisms and $F$-harmonic maps.

An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic (i.e, minimal). In a later paper [CMO2], Cadeo-Monttaldo-Oniciuc shown that the theo…

Study on $(λ,λ)$-eigenfunctions on compact manifolds, showing manifold properties and eigenfamily dimensions.

Maps between Riemannian manifolds which are submersions on a dense subset, are studied by means of the eigenvalues of the pull-back of the target metrics, the first fundamental form. Expressions for the derivatives of these eigenvalues yield characterizations of harmonicity, totally geodesic maps and biconformal change…

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 …

We study bifurcation for the constant scalar curvature equation along a one-parameter family of Riemannian metrics on the total space of a harmonic Riemannian submersion. We provide an existence theorem for bifurcation points and a criterion to see that the conformal factors corresponding to the bifurcated metrics must…

As a generalization of slant submersions (Sahin, 2011), semi-slant submersions (Park and Prasad), and slant Riemannian maps (Sahin), we define the notion of semi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We study the integrability of distributions, the geometry of fibers, the harmon…

New rigidity result for maps between curved spaces.

The paper proves non-existence results for λ-biharmonic submersions from curved manifolds.

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.

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…

We introduce conformal anti-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 find necessary and sufficient conditions for a conformal anti-invariant submersion to b…

As a generalization of slant Riemannian maps (Sahin), semi-slant Riemannian maps (Park), almost h-slant submersions (Park 2012), and almost h-semi-slant submersions (Park 2011), we introduce the notion of almost h-semi-slant Riemannian maps from almost quaternionic Hermitian manifolds to Riemannian manifolds. We invest…

We study anti-holomorphic semi-invariant submersions from Kählerian manifolds onto Riemannian manifolds. We prove that all distributions which are involved in the definition of the submersion are integrable. We also prove that the O'Neill's tensor $\mathcal{T}$ vanishes on the invariant vertical distribution. We give n…

The paper studies $f$-biharmonic maps and submersions in space forms.

We deform a map into a Riemannian manifold that is horizontal with respect to a submersion onto a non-positively curved manifold and satisfies a Chow condition into a harmonic one through a horizontal homotopy.

The paper introduces and studies a new type of submersion in Riemannian geometry.

The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.

We prove that harmonic PHH submersions are (weakly) stable.

Let $π:(E,\nabla^{E}) \to (M,g)$ be an affine submersion with horizontal distribution, where $\nabla^{E}$ is a symmetric connection and $M$ is a Riemannian manifold. Let $σ$ be a section of $π$, namely, $π\circ σ= Id_{M}$. It is possible to study the harmonic property of section $σ$ in two ways. First, we see $σ$ as a …

We construct a new class of biharmonic maps, which are the critical points for the bienergy functional, by deforming conformally the codomain metric of harmonic Riemannian submersions such that they become nonharmonic but biharmonic.

The variational theory of higher-power energy is developed for mappings between Riemannian manifolds, and more generally sections of submersions of Riemannian manifolds, and applied to sections of Riemannian vector bundles and their sphere subbundles. A complete classification is then given for left-invariant vector fi…

We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions.

New concept of $V$-minimality applied to Kaehler and non-Kaehler manifolds.

J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studies in the area. In this paper, We study k-harmonic immersion into a sphere, and get the rerationship between radious and "k"…

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…

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…