scholarly journals Conformal semi-invariant Riemannian maps from almost Hermitian manifolds

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1125-1134
Author(s):  
Bayram Şahina ◽  
Şener Yanan
Keyword(s):  
Riemannian Manifolds ◽  
Kaehler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Pluriharmonic Maps

Conformal semi-invariant Riemannian maps from Kaehler manifolds to Riemannian manifolds are introduced. We give examples, study the geometry of leaves of certain distributions and investigate certain conditions for such maps to be horizontally homothetic. Morever, we introduce special pluriharmonic maps and obtain characterizations.

scholarly journals ANTI-INVARIANT RIEMANNIAN SUBMERSIONS FROM LOCALLY CONFORMAL KAEHLER MANIFOLDS

2021 ◽  
pp. 1031
Author(s):  
Majid Ali Choudhary ◽  
Lamia Saeed Alqahtani
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Locally Conformal

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.

scholarly journals Bi-slant submersions in complex geometry

2020 ◽  
Vol 17 (04) ◽  
pp. 2050055
Author(s):  
Cem Sayar ◽  
Mehmet Akif Akyol ◽  
Rajendra Prasad
Keyword(s):  
Riemannian Manifolds ◽  
Complex Geometry ◽  
Base Space ◽  
Total Space ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

In this paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We mainly focus on bi-slant submersions from Kaehler manifolds. We provide a proper example of bi-slant submersion, investigate the geometry of foliations determined by vertical and horizontal distributions, and obtain the geometry of leaves of these distributions. Moreover, we obtain curvature relations between the base space, the total space and the fibers, and find geometric implications of these relations.

SEMI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2011 ◽  
Vol 08 (07) ◽  
pp. 1439-1454 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
Necessary And Sufficient Conditions ◽  
Classification Theorem ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Riemannian Map ◽  
Necessary And Sufficient

This paper has two aims. First, we show that the usual notion of umbilical maps between Riemannian manifolds does not work for Riemannian maps. Then we introduce a new notion of umbilical Riemannian maps between Riemannian manifolds and give a method on how to construct examples of umbilical Riemannian maps. In the second part, as a generalization of CR-submanifolds, holomorphic submersions, anti-invariant submersions, invariant Riemannian maps and anti-invariant Riemannian maps, we introduce semi-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples and investigate the geometry of distributions which are arisen from definition. We also obtain a decomposition theorem and give necessary and sufficient conditions for a semi-invariant Riemannian map to be totally geodesic. Then we study the geometry of umbilical semi-invariant Riemannian maps and obtain a classification theorem for such Riemannian maps.

Vector Fields and Infinitesimal Transformations on Almost-Hermitian Manifolds with Boundary

1965 ◽  
Vol 17 ◽  
pp. 213-238
Author(s):  
Arthur L. Hilt ◽  
Chuan-Chih Hsiung
Keyword(s):  
Riemannian Manifolds ◽  
Vector Fields ◽  
Manifolds With Boundary ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Infinitesimal Transformations

Many authors have made interesting and important contributions to the study of vector fields or infinitesimal transformations on compact orientable Riemannian manifolds and Hermitian manifolds without boundary. Recently, Hsiung (6, 7, 8) has extended some of these results to compact orientable Riemannian manifolds with boundary. The purpose of this paper is to continue Hsiung's work by studying vector fields and infinitesimal transformations on almost-Hermitian manifolds with boundary.

SLANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2012 ◽  
Vol 10 (02) ◽  
pp. 1250080 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Projective Space ◽  
Riemannian Manifolds ◽  
Complex Projective Space ◽  
Harmonic Maps ◽  
Sufficient Conditions ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Necessary And Sufficient ◽  
Complex Projective

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficient conditions for slant Riemannian maps to be totally geodesic. Moreover, we relate the notion of slant Riemannian maps to the notion of pseudo horizontally weakly conformal (PHWC) maps which are useful for proving various complex-analytic properties of stable harmonic maps from complex projective space.

Isometric Immersions of almost Hermitian Manifolds

1969 ◽  
Vol 21 ◽  
pp. 456-459
Author(s):  
Alfred Gray
Keyword(s):  
Riemannian Manifolds ◽  
Positive Curvature ◽  
Metric Tensor ◽  
Compact Symmetric Space ◽  
Hermitian Manifolds ◽  
Cw Complex ◽  
Almost Hermitian Manifolds ◽  
Image Position ◽  
Simply Connected ◽  
Hyperplane Sections

The Lefschetz theorem on hyperplane sections, as proved by Andreotti and Frankel (1), depends upon the following result.THEOREM. If M is a non-singular affine algebraic variety of real dimension 2k of complex n-space, thenThis theorem, which is interesting in itself, has been strengthened by Milnor (7), who showed that M has the homotopy type of a k-dimensional CW-complex.In this paper we generalize the above theorem in two directions. First, we replace complex n-space by some other complete simply connected Riemannian manifold which either has non-positive curvature or is a compact symmetric space. Secondly, we allow M and to be quasi-Kâhlerian (see below) instead of Kählerian.We first introduce some notation. Let M and be C∞ Riemannian manifolds with M isometrically immersed in . Denote by 〈, 〉 the metric tensor of either M or .

scholarly journals Semi-invariant Submersions from Almost Hermitian Manifolds

2013 ◽  
Vol 56 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Bayram Ṣahin
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Definition Of ◽  
Necessary And Sufficient

AbstractWe introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semiinvariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.

A SCHWARZ LEMMA FOR -HARMONIC MAPS AND THEIR APPLICATIONS

2017 ◽  
Vol 96 (3) ◽  
pp. 504-512 ◽  
Author(s):  
QUN CHEN ◽  
GUANGWEN ZHAO
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Schwarz Lemma ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Holomorphic Maps ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Almost Kähler

We establish a Schwarz lemma for $V$-harmonic maps of generalised dilatation between Riemannian manifolds. We apply the result to obtain corresponding results for Weyl harmonic maps of generalised dilatation from conformal Weyl manifolds to Riemannian manifolds and holomorphic maps from almost Hermitian manifolds to quasi-Kähler and almost Kähler manifolds.

Conformal semi-slant submersions

2017 ◽  
Vol 14 (07) ◽  
pp. 1750114 ◽  
Author(s):  
Mehmet Akif Akyol
Keyword(s):  
Riemannian Manifolds ◽  
Totally Geodesic ◽  
Base Manifold ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Product Structures

Park and Prasad [Semi-slant submersions, Bull. Korean Math. Soc. 50(3) (2013) 951–962.] defined and studied semi-slant submersions as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions. As a generalization of semi-slant submersions, we introduce conformal semi-slant submersions and study the new submersions from almost Hermitian manifolds onto Riemannian manifolds. We study the integrability of ditributions and the geometry of leaves of a conformal submersion. Moreover, we show that there are certain product structures on base manifold of a conformal semi-slant submersion. We also obtain totally geodesic conditions for such maps. Finally, we give lots of examples.

INVARIANT AND ANTI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2010 ◽  
Vol 07 (03) ◽  
pp. 337-355 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Riemannian Manifolds ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Riemannian Map ◽  
Definition Of ◽  
Totally Real

As a generalization of isometric immersions and Riemannian submersions, Riemannian maps were introduced by Fischer [Riemannian maps between Riemannian manifolds, Contemp. Math.132 (1992) 331–366]. It is known that a real valued Riemannian map satisfies the eikonal equation which provides a bridge between physical optics and geometrical optics. In this paper, we introduce invariant and anti-invariant Riemannian maps between Riemannian manifolds and almost Hermitian manifolds as a generalization of invariant immersions and totally real immersions, respectively. Then we give examples, present a characterization and obtain a geometric characterization of harmonic invariant Riemannian maps in terms of the distributions which are involved in the definition of such maps. We also give a decomposition theorem by using the existence of invariant Riemannian maps to Kähler manifolds. Moreover, we study anti-invariant Riemannian maps, give examples and obtain a classification theorem for umbilical anti-invariant Riemannian maps.

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