On Quasi-Hemi-Slant Riemannian Maps

2003

In this note we give some geometrical and analytical properties which caracterise the quasiconformal maps in Riemannian manifolds.

Kuwait Journal of Science, 2015

In this paper, we introduce slant submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic.

Turkish Journal of Mathematics

In this paper, we define the concept of almost product Riemannian submersion between almost product Riemannian manifolds. We introduce slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations that arise from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic.

Turkish Journal of Mathematics

An interesting class of submanifolds of almost Hermitian manifolds (M˜ , g˜, J) is the class of slant submanifolds. Slant submanifolds were introduced by the first author in [6] as submanifolds M of (M˜ , g˜, J) such that, for any nonzero vector X ∈ TpM, p ∈ M, the angle θ(X) between JX and the tangent space TpM is independent of the choice of p ∈ M and X ∈ TpM. The first results on slant submanifolds were summarized in the book [7]. Since then slant submanifolds have been studied by many geometers. Many nice results on slant submanifolds have been obtained during the last two decades. The main purpose of this paper is to study pointwise slant submanifolds in almost Hermitian manifolds which extends slant submanifolds in a very natural way. Several basic results in this respect are proved in this paper.

Publicationes mathematicae

We study the relationship between slant submanifolds in both Complex and Contact Geometry through Riemannian submersions. We present some construction procedures to obtain slant submanifolds in the unit sphere and in a Stiefel manifold. We also generalize them by means of the Boothby-Wang fibration. Finally, we show characterization theorems of three-dimensional slant submanifolds.

Pacific Journal of Mathematics, 2002

The purpose of this paper is to study the relations between quasiregular mappings on Riemannian manifolds and differential forms. Four classes of differential forms are introduced and it is shown that some differential expressions connected in a natural way to quasiregular mappings are members in these classes.

arXiv (Cornell University), 2022

We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove geometrical inequalities for a sub-Riemannian submanifold. As applications, inequalities are proved for submanifolds with mutually orthogonal distributions that include scalar and mutual curvature. For compact submanifolds, inequalities are obtained that are supported by known integral formulas for almost-product manifolds.

Ukrainian Mathematical Journal, 2016

UDC 517.9 We introduce slant lightlike submersions from an indefinite almost Hermitian manifold into a lightlike manifold. We establish the existence theorems for these submersions and investigate the necessary and sufficient conditions for the leaves of the distributions to be totally geodesic foliations in indefinite almost Hermitian manifolds.

Manifolds - Current Research Areas, 2017

In this chapter, we introduce the theory of sub-manifolds of a Riemannian manifold. The fundamental notations are given. The theory of sub-manifolds of an almost Riemannian product manifold is one of the most interesting topics in differential geometry. According to the behaviour of the tangent bundle of a sub-manifold, with respect to the action of almost Riemannian product structure of the ambient manifolds, we have three typical classes of sub-manifolds such as invariant sub-manifolds, anti-invariant sub-manifolds and semi-invariant sub-manifolds. In addition, slant, semi-slant and pseudo-slant sub-manifolds are introduced by many geometers.

Mediterranean Journal of Mathematics, 2015

As a generalization of anti-invariant submersions, semiinvariant submersions and slant submersions, we introduce the notion of hemi-slant submersion and study such submersions from Kählerian manifolds onto Riemannian manifolds. After we study the geometry of leaves of distributions which are involved in the definition of the submersion, we obtain new conditions for such submersions to be harmonic and totally geodesic. Moreover, we give a characterization theorem for the proper hemi-slant submersions with totally umbilical fibers.

International Journal of Geometric Methods in Modern Physics, 2020

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.

The Korean Journal of Mathematics, 2020

We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

Filomat, 2018

We derive two mixed systems of Cauchy type in covariant derivatives of the first and second kind that ensures the existence of almost geodesic mappings of the second type between manifolds with non-symmetric linear connection. Also, we consider a particular class of these mappings determined by the condition ∇F = 0, where ∇ is the symmetric part of non-symmetric linear connection ∇ 1 and F is the affinor structure. The same special class of almost geodesic mappings of the second type between generalized Riemannian spaces was recently considered in the paper M.Z. Petrović, Special almost geodesic mappings of the second type between generalized Riemannian spaces, Bull. Malays. Math. Sci. Soc. (2),

Journal of Function Spaces and Applications, 2013

We introduce anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds onto semi-Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a semi-Riemannian submersion, and check the harmonicity of such submersions. We also obtain curvature relations between the base manifold and the total manifold.