Nearly cosymplectic manifolds with nullity conditions

2019 ◽  
Vol 12 (06) ◽  
pp. 2040012 ◽  
Author(s):  
Mustafa Yıldırım ◽  
Gülhan Ayar
Keyword(s):  
Cosymplectic Manifold ◽  
Projectively Flat ◽  
Cosymplectic Manifolds ◽  
Nullity Distribution ◽  
Nearly Cosymplectic ◽  
Text Condition

We investigate nearly cosymplectic manifolds with [Formula: see text]-nullity distribution. Also, we consider pseudo-projectively flat [Formula: see text]-nearly cosymplectic manifold and study [Formula: see text] condition.

scholarly journals Warped Product Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Siraj Uddin ◽  
S. H. Kon ◽  
M. A. Khan ◽  
Khushwant Singh
Keyword(s):  
Warped Product ◽  
Riemannian Product ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Invariant Submanifolds ◽  
Nearly Cosymplectic

We study warped product semi-invariant submanifolds of nearly cosymplectic manifolds. We prove that the warped product of the type is a usual Riemannian product of and , where and are anti-invariant and invariant submanifolds of a nearly cosymplectic manifold , respectively. Thus we consider the warped product of the type and obtain a characterization for such type of warped product.

scholarly journals Some Remarks on Quasi-Generalized CR-Null Geometry in Indefinite Nearly Cosymplectic Manifolds

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Fortuné Massamba ◽  
Samuel Ssekajja
Keyword(s):  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Nearly Cosymplectic ◽  
Geometric Effects

Attention is drawn to some distributions on ascreen Quasi-Generalized Cauchy-Riemannian (QGCR) null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finally discuss the geometric effects of geodesity conditions on such submanifolds.

scholarly journals Noninvariant Hypersurfaces of a Nearly Trans-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Satya Prakash Yadav ◽  
Shyam Kishor
Keyword(s):  
Contact Structure ◽  
Sasakian Manifold ◽  
Necessary Condition ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Nearly Cosymplectic

The present paper focuses on the study of noninvariant hypersurfaces of a nearly trans-Sasakian manifold equipped with(f,g,u,v,λ)-structure. Initially some properties of this structure have been discussed. Further, the second fundamental forms of noninvariant hypersurfaces of nearly trans-Sasakian manifolds and nearly cosymplectic manifolds with(f,g,u,v,λ)-structure have been calculated providedfis parallel. In addition, the eigenvalues offhave been found and proved that a noninvariant hypersurface with(f,g,u,v,λ)-structure of nearly cosymplectic manifold with contact structure becomes totally geodesic. Finally the paper has been concluded by investigating the necessary condition for totally geodesic or totally umbilical noninvariant hypersurface with(f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold.

scholarly journals A Geometric Obstruction for CR-Slant Warped Products in a Nearly Cosymplectic Manifold

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1622
Author(s):  
Siraj Uddin ◽  
M. Z. Ullah
Keyword(s):  
20Th Century ◽  
Fundamental Form ◽  
Second Fundamental Form ◽  
Early 20Th Century ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Nearly Cosymplectic

In the early 20th century, B.-Y. Chen introduced the concept of CR-warped products and obtained several fundamental results, such as inequality for the length of second fundamental form. In this paper, we obtain B.-Y. Chen’s inequality for CR-slant warped products in nearly cosymplectic manifolds, which are the more general classes of manifolds. The equality case of this inequality is also investigated. Furthermore, the inequality is discussed for some important subclasses of CR-slant warped products.

Ricci solitons on 3-dimensional cosymplectic manifolds

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Ricci Solitons ◽  
Cosymplectic Manifold ◽  
3 Dimensional ◽  
Cosymplectic Manifolds

AbstractIn this paper, we prove that if a 3-dimensional cosymplectic manifold

scholarly journals A note on warped product submanifolds of cosymplectic manifolds

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 95-102 ◽  
Author(s):  
Siraj Uddin ◽  
V.A. Khan ◽  
K.A. Khan
Keyword(s):  
Warped Product ◽  
Warped Products ◽  
Cosymplectic Manifold ◽  
Slant Submanifolds ◽  
Cosymplectic Manifolds

In this paper, we study warped product anti-slant submanifolds of cosymplectic manifolds. It is shown that the cosymplectic manifold do not admit non trivial warped product submanifolds in the form N??f N? and then we obtain some results for the existence of warped products of the type N??f N?, where N? and N? are anti-invariant and proper slant submanifolds of a cosymplectic manifold M?, respectively.

scholarly journals On nearly Sasakian and nearly cosymplectic manifolds

2017 ◽  
Vol 197 (1) ◽  
pp. 127-138 ◽  
Author(s):  
Antonio De Nicola ◽  
Giulia Dileo ◽  
Ivan Yudin
Keyword(s):  
Cosymplectic Manifolds ◽  
Nearly Sasakian ◽  
Nearly Cosymplectic
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