ALMOST SEMI-INVARIANT SUBMANIFOLDS OF A COSYMPLECTIC MANIFOLD

1986 ◽  
Vol 19 (2) ◽  
Author(s):  
A. Cabras ◽  
P. Matzeu
Keyword(s):  
Cosymplectic Manifold ◽  
Invariant Submanifolds

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 Warped product CR-submanifolds of LP-cosymplectic manifolds

Filomat ◽  
2010 ◽  
Vol 24 (1) ◽  
pp. 87-95 ◽  
Author(s):  
Siraj Uddin
Keyword(s):  
Warped Product ◽  
Characterization Result ◽  
Cosymplectic Manifold ◽  
Cr Submanifold ◽  
Cosymplectic Manifolds ◽  
Subject Classifications ◽  
Invariant Submanifolds ◽  
Mathematics Subject Classifications ◽  
Cr Submanifolds

In this paper, we study warped product CR-submanifolds of LP-cosymplectic manifolds. We have shown that the warped product of the type M = NT ? fN? does not exist, where NT and N? are invariant and anti-invariant submanifolds of an LP-cosymplectic manifold M?, respectively. Also, we have obtained a characterization result for a CR-submanifold to be locally a CR-warped product. 2010 Mathematics Subject Classifications. 53C15, 53C40, 53C42. .

A note on invariant submanifolds of CR-integrable almost Kenmotsu manifolds

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6211-6218 ◽  
Author(s):  
Young Suh ◽  
Krishanu Mandal ◽  
Uday De
Keyword(s):  
Invariant Submanifold ◽  
Kenmotsu Manifold ◽  
Totally Geodesic ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Invariant Submanifolds

The present paper deals with invariant submanifolds of CR-integrable almost Kenmotsu manifolds. Among others it is proved that every invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold with k < -1 is totally geodesic. Finally, we construct an example of an invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold which is totally geodesic.

Semi-invariant submanifolds of a normal almost paracontact manifold

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4875-4887 ◽  
Author(s):  
Mehmet Atçeken ◽  
Siraj Uddin
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fundamental Properties ◽  
Invariant Submanifolds ◽  
Normal Almost Paracontact Manifold ◽  
Necessary And Sufficient

In this paper, we introduce the notion of semi-invariant submanifolds of a normal almost paracontact manifold. We study their fundamental properties and the particular cases. The necessary and sufficient conditions are given for a submanifold to be invariant or anti-invariant. Also, we give some results for semi-invariant submanifolds of a normal almost paracontact manifold with constant c and we construct an example.

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 On Lie algebras of vector fields with invariant submanifolds

1974 ◽  
Vol 55 ◽  
pp. 91-110 ◽  
Author(s):  
Akira Koriyama
Keyword(s):  
Lie Algebras ◽  
Compact Support ◽  
Vector Fields ◽  
Finite Dimensional ◽  
Invariant Submanifolds ◽  
Infinitesimal Automorphisms

It is known (Pursell and Shanks [9]) that an isomorphism between Lie algebras of infinitesimal automorphisms of C∞ structures with compact support on manifolds M and M′ yields an isomorphism between C∞ structures of M and M’.Omori [5] proved that this is still true for some other structures on manifolds. More precisely, let M and M′ be Hausdorff and finite dimensional manifolds without boundary. Let α be one of the following structures:

scholarly journals Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 246
Author(s):  
Yan Zhao ◽  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Ricci Operator ◽  
Cosymplectic Manifold

Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.

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