scholarly journals On Quasi-Hemi-Slant Riemannian Submersion

2019 ◽  
pp. 1-14
Author(s):  
S. Longwap ◽  
F. Massamba ◽  
N. E. Homti
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Riemannian Submersions ◽  
Almost Hermitian Manifold ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

We recall the notions of invariant, anti-invarian, semi-invariant, slant, semi-slant, quasi-slant and hemi-slant Riemannian submersions from almost Hermitian manifolds to a Riemannian manifolds. In this paper we contruct a Riemannian submersion which generalizes hemi-slant, semi-slant and semi-invariant Riemanian submersions from almost Hermitian manifold to a Riemannian manifold and study its geometry.

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.

scholarly journals Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yılmaz Gündüzalp
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Riemannian Submersions ◽  
Base Manifold ◽  
Hermitian Manifolds ◽  
Definition Of

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.

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.

scholarly journals On Kähler-like and G-Kähler-like almost Hermitian manifolds

2020 ◽  
Vol 7 (1) ◽  
pp. 145-161
Author(s):  
Masaya Kawamura
Keyword(s):  
Complex Structure ◽  
Hermitian Manifold ◽  
Almost Complex Structure ◽  
Almost Hermitian Manifold ◽  
Hermitian Manifolds ◽  
Almost Complex ◽  
Almost Hermitian Manifolds ◽  
Balanced Metric

AbstractWe introduce Kähler-like, G-Kähler-like metrics on almost Hermitian manifolds. We prove that a compact Kähler-like and G-Kähler-like almost Hermitian manifold equipped with an almost balanced metric is Kähler. We also show that if a Kähler-like and G-Kähler-like almost Hermitian manifold satisfies B_{\bar i\bar j}^\lambda B_{\lambda j}^i \ge 0, then the metric is almost balanced and the almost complex structure is integrable, which means that the metric is balanced. We investigate a G-Kähler-like almost Hermitian manifold under some assumptions.

Scalar curvature of Lagrangian Riemannian submersions and their harmonicity

2017 ◽  
Vol 14 (12) ◽  
pp. 1750171 ◽  
Author(s):  
Şemsi Eken Meri̇ç ◽  
Erol Kiliç ◽  
Yasemi̇n Sağiroğlu
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Necessary And Sufficient

In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion [Formula: see text] has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.

scholarly journals Contact-Complex Riemannian Submersions

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 2996
Author(s):  
Cornelia-Livia Bejan ◽  
Şemsi Eken Meriç ◽  
Erol Kılıç
Keyword(s):  
Riemannian Submersion ◽  
Ricci Soliton ◽  
Hermitian Manifold ◽  
Horizontal Distribution ◽  
The Other ◽  
Riemannian Submersions ◽  
Almost Hermitian Manifold ◽  
Base Manifold ◽  
Contact Complex ◽  
Contact Riemannian Manifold

A submersion from an almost contact Riemannian manifold to an almost Hermitian manifold, acting on the horizontal distribution by preserving both the metric and the structure, is, roughly speaking a contact-complex Riemannian submersion. This paper deals mainly with a contact-complex Riemannian submersion from an η-Ricci soliton; it studies when the base manifold is Einstein on one side and when the fibres are η-Einstein submanifolds on the other side. Some results concerning the potential are also obtained here.

scholarly journals On the Kähler-likeness on almost Hermitian manifolds

2019 ◽  
Vol 6 (1) ◽  
pp. 366-376
Author(s):  
Masaya Kawamura
Keyword(s):  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Hermitian Metric ◽  
Kähler Metric ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Kahler Metric

AbstractWe define a Kähler-like almost Hermitian metric. We will prove that on a compact Kähler-like almost Hermitian manifold (M2n, J, g), if it admits a positive ∂ ̄∂-closed (n − 2, n − 2)-form, then g is a quasi-Kähler metric.

scholarly journals Generic riemannian submersions

2013 ◽  
Vol 44 (4) ◽  
pp. 395-409 ◽  
Author(s):  
Tanveer Fatima ◽  
Shahid Ali
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Generic Product ◽  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Almost Hermitian Manifold ◽  
Definition Of ◽  
Necessary And Sufficient

B. Sahin [12] introduced the notion of semi-invariant Riemannian submersions as a generalization of anti-invariant Riemmanian submersions [11]. As a generalization to semi-invariant Riemannian submersions we introduce the notion of generic submersion from an almost Hermitian manifold onto a Riemannian manifold and investigate the geometry of foliations which arise from the definition of a generic Riemannian submersion and find necessary and sufficient condition for total manifold to be a generic product manifold. We also find necessary and sufficient conditions for a generic submersion to be totally geodesic.

scholarly journals A useful orthonormal basis on bi-slant submanifolds of almost Hermitian manifolds

2016 ◽  
Vol 47 (2) ◽  
pp. 143-161 ◽  
Author(s):  
Mehmet Gulbahar ◽  
Erol Kilic ◽  
Sadik Keles
Keyword(s):  
Orthonormal Basis ◽  
Complex Space ◽  
Space Form ◽  
Hermitian Manifold ◽  
Complex Space Form ◽  
Slant Submanifold ◽  
Almost Hermitian Manifold ◽  
Slant Submanifolds ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

In this paper, we study bi-slant submanifolds of an almost Hermitian manifold for different cases. We introduce a new orthonormal basis on bi-slant submanifold, semi-slant submanifold and hemi-slant submanifold of an almost Hermitian manifold to compute Chen's main inequalities. We investigate these inequalities for semi-slant submanifolds, hemi-slant submanifolds and slant submanifolds of a generalized complex space form. We obtain some characterizations on such submanifolds of a complex space form.

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