Anti-invariant Riemannian Submersions Research Articles

Chen–Ricci inequality for anti-invariant Riemannian submersions from conformal Kenmotsu space form

Chen–Ricci inequality for anti-invariant Riemannian submersions from conformal Kenmotsu space form

On Optimal Inequalities for Anti-invariant Riemannian Submersions from Conformal Sasakian Space Forms

On Optimal Inequalities for Anti-invariant Riemannian Submersions from Conformal Sasakian Space Forms

B. Y. Chen-Ricci inequalities for anti-invariant Riemannian submersions in Kenmotsu space forms

The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms Ks(ε)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{s}(\\varepsilon )$$\\end{document}. We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. Moreover, we acquire Chen-Ricci inequalities on the kerϑ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ker \\vartheta _{*}$$\\end{document} and (kerϑ∗)⊥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\ker \\vartheta _{*})^{\\bot }$$\\end{document} distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}.

A Special Type of Anti-invariant Riemannian Submersions

A Special Type of Anti-invariant Riemannian Submersions

Curvature Invariants for Anti-invariant Riemannian Submersions from Cosymplectic Space Forms

Curvature Invariants for Anti-invariant Riemannian Submersions from Cosymplectic Space Forms

Hemi-slant Riemannian submersions from cosymplectic manifolds

At this work, our main objective is to present the idea of hemi-slant Riemannian submersions from almost contact metric manifolds as a natural generalization of anti-invariant Riemannian submersions, semi-invariant Riemannian submersions and slant Riemannian submersions. We mostly examined on hemi-slant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. During this way, we tend to study and investigate integrability conditions, the geometry of leaves of distributions which are emerged from the definition of the submersion. Besides, we tend to get new conditions for these submersions to be totally geodesic. Finally, we construct some quality examples of such submersion.

Some inequalities of anti-invariant Riemannian submersions in complex space forms

The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in complex space forms.

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.

Sharp inequalities for anti-invariant Riemannian submersions from Sasakian space forms

We obtain sharp inequalities involving the Ricci curvature and the scalar curvature for anti-invariant Riemannian submersions from Sasakian space forms onto Riemannian manifolds.

ANTI-INVARIANT RIEMANNIAN SUBMERSIONS FROM LOCALLY CONFORMAL KAEHLER MANIFOLDS

Recently, Sahin [10] studied the anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In present work, these notions of anti-invariant and Lagrangian Riemannian submersions have been extended to locally conformal Kaehler manifolds. Certain decomposition results and the geometry of foliation have also been investigated.

Anti-invariant Riemanian submersions from nearly-k-cosymplectic manifolds

In this paper, we introduce anti-invariant Riemannian submersions from nearly-K-cosymplectic manifolds onto Riemannian manifolds. We study the integrability of horizontal distributions. And we investigate the necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. Moreover, we give examples of anti-invariant Riemannian submersions such that characteristic vector field ? is vertical or horizontal.

English

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: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples of such maps. Finally, we obtain some types of decomposition theorems.

On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian

In this paper, we study Riemannian, anti-invariant and Lagrangian submersions from locally product Riemannian manifolds onto Riemannian manifolds. We first give a characterization theorem for Riemannian submersions. It is proved that the fibers of a Lagrangian submersion are always totally geodesic. We also consider the first variational formula of anti-invariant Riemannian submersions and give a new condition for the harmonicity of such submersions.

Anti-invariant Riemannian Submersions: A Lie-theoretical Approach

We give a construction which is Lie theoretic of anti-invariant Riemannian submersions from almost Hermitian manifolds, from quaternion manifolds, from para-Hermitian manifolds, from para-quaternion manifolds, and from octonian manifolds. This yields many compact Einstein examples.

Anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds

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 the nonexistence of (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that the characteristic vector field $\xi $ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, we presented an example of anti-invariant Riemannian submersions in the case where the characteristic vector field $\xi $ is a horizontal vector field and an anti-invariant horizontally conformal submersion such that $\xi $ is a vertical vector field.

EINSTEIN CONDITIONS FOR THE BASE SPACE OF ANTI-INVARIANT RIEMANNIAN SUBMERSIONS AND CLAIRAUT SUBMERSIONS

In this paper, we study the geometry of anti-invariant Riemanniansubmersions from a Kahler manifold onto a Riemannian manifold. Wefirst determine the base space when the total space of ananti-invariant Riemannian submersion is Einstein and then weinvestigate new conditions for anti-invariant Riemannian submersionsto be Clairaut submersions. We also focus on the geometry ofClairaut anti-invariant submersions.

Product theorems on anti-invariant Riemannian submersions

In Ali and Fatima (J Tensor Soc 6(2):163–175, 2012) we studied anti-invariant and Langrangian Riemannian submersions from nearly kaehler manifolds. In this paper we have continued the study of such submersion and investigate the geometry of the leaves of two distributions and obtain the necessary and sufficient conditions for a Langrangian Riemannian submersions to be totally geodesic map. In the end, the decomposition theorems for the total manifold of the submersion are obtained.

Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds

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 geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field ? is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian submersions.

Anti-invariant Riemannian submersions from a locally Riemannian product manifold to any Riemannian manifold

In this paper, we define and study anti-invariant Riemannian submersions from a locally Riemannian product manifold onto a Riemannian manifold. We investigate the geometric properties of distributions which are involved from the definition of an anti-invariant Riemannian submersions in locally Riemannian product manifolds.

Anti-invariant Riemannian submersions from nearly Kaehler manifolds

We extend the notion of anti-invariant and Langrangian Riemannian submersion to the case when the total manifold is nearly Kaehler. We obtain the integrability conditions for the horizontal distribution while it is noted that the vertical distribution is always integrable. We also investigate the geometry of the foliations of the two distributions and obtain the necessary and sufficient condition for a Langrangian submersion to be totally geodesic. The decomposition theorems for the total manifold of the submersion are obtained.