scholarly journals On a class of exact locally conformal cosymlectic manifolds

1996 ◽  
Vol 19 (2) ◽  
pp. 267-278
Author(s):  
I. Mihai ◽  
L. Verstraelen ◽  
R. Rosca
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Conformal Transformation ◽  
Space Form ◽  
Conformal Vector Field ◽  
Cosymplectic Manifold ◽  
Almost Cosymplectic Manifold ◽  
Riemannian Connection ◽  
Locally Conformal ◽  
Hyperbolic Space Form

An almost cosymplectic manifoldMis a(2m+1)-dimensional oriented Riemannian manifold endowed with a 2-formΩof rank2m, a 1-formηsuch thatΩm Λ η≠0and a vector fieldξsatisfyingiξΩ=0andη(ξ)=1. Particular cases were considered in [3] and [6].Let(M,g)be an odd dimensional oriented Riemannian manifold carrying a globally defined vector fieldTsuch that the Riemannian connection is parallel with respect toT. It is shown that in this caseMis a hyperbolic space form endowed with an exact locally conformal cosymplectic structure. MoreoverTdefines an infinitesimal homothety of the connection forms and a relative infinitesimal conformal transformation of the curvature forms.The existence of a structure conformal vector fieldConMis proved and their properties are investigated. In the last section, we study the geometry of the tangent bundle of an exact locally conformal cosymplectic manifold.

scholarly journals On Riemannian manifolds endowed with a locally conformal cosymplectic structure

2005 ◽  
Vol 2005 (21) ◽  
pp. 3471-3478
Author(s):  
Ion Mihai ◽  
Radu Rosca ◽  
Valentin Ghişoiu
Keyword(s):  
Vector Field ◽  
Lie Algebra ◽  
Riemannian Manifolds ◽  
Gauss Map ◽  
Cosymplectic Manifold ◽  
Cosymplectic Structure ◽  
Locally Conformal ◽  
Infinitesimal Transformations ◽  
Conformal Contact

We deal with a locally conformal cosymplectic manifoldM(φ,Ω,ξ,η,g)admitting a conformal contact quasi-torse-forming vector fieldT. The presymplectic2-formΩis a locally conformal cosymplectic2-form. It is shown thatTis a3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of∧Mare investigated. The Gauss map of the hypersurfaceMξnormal toξis conformal andMξ×Mξis a Chen submanifold ofM×M.

scholarly journals Almost Cosymplectic $$(k,\mu )$$-metrics as $$\eta$$-Ricci Solitons

2021 ◽  
Author(s):  
Wenjie Wang
Keyword(s):  
Vector Field ◽  
Lie Group ◽  
Local Structure ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Contact Transformation ◽  
Potential Vector ◽  
Cosymplectic Manifold ◽  
Almost Cosymplectic Manifold ◽  
Potential Vector Field

AbstractIn this paper, we study $$\eta$$ η -Ricci solitons on almost cosymplectic $$(k,\mu )$$ ( k , μ ) -manifolds. As an application, it is proved that if an almost cosymplectic $$(k,\mu )$$ ( k , μ ) -metric with $$k<0$$ k < 0 represents a Ricci soliton, then the potential vector field of the Ricci soliton is a strict infinitesimal contact transformation, and the corresponding almost cosymplectic manifold is locally isometric to a Lie group whose local structure is determined completely by $$k<0$$ k < 0 . In addition, a concrete example is constructed to illustrate the above result.

scholarly journals A note on Chen's basic equality for submanifolds in a Sasakian space form

2003 ◽  
Vol 2003 (11) ◽  
pp. 711-716 ◽  
Author(s):  
Mukut Mani Tripathi ◽  
Jeong-Sik Kim ◽  
Seon-Bu Kim
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Sectional Curvature ◽  
Space Form ◽  
Sasakian Space Form ◽  
Invariant Submanifold ◽  
Basic Equality

It is proved that a Riemannian manifoldMisometrically immersed in a Sasakian space formM˜(c)of constantφ-sectional curvaturec<1, with the structure vector fieldξtangent toM, satisfies Chen's basic equality if and only if it is a3-dimensional minimal invariant submanifold.

scholarly journals Inequality for Ricci curvature of certain submanifolds in locally conformal almost cosymplectic manifolds

2005 ◽  
Vol 2005 (10) ◽  
pp. 1621-1632 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Slant Submanifold ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Arbitrary Codimension ◽  
Locally Conformal

We establish inequalities between the Ricci curvature and the squared mean curvature, and also between thek-Ricci curvature and the scalar curvature for a slant, semi-slant, and bi-slant submanifold in a locally conformal almost cosymplectic manifold with arbitrary codimension.

scholarly journals Closed conformal vector fields on pseudo-Riemannian manifolds

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
D. A. Catalano
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Geometric Proof ◽  
Conformal Vector Field ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Local Coordinates

We give here a geometric proof of the existence of certain local coordinates on a pseudo-Riemannian manifold admitting a closed conformal vector field.

scholarly journals Locally Conformal Almost Cosymplectic Manifold of Φ-holomorphic Sectional Conharmonic Curvature Tensor

2018 ◽  
Vol 11 (3) ◽  
pp. 671-681 ◽  
Author(s):  
Habeeb Mtashar Abood ◽  
Farah Al-Hussaini
Keyword(s):  
Curvature Tensor ◽  
Einstein Manifold ◽  
Cosymplectic Manifold ◽  
Almost Cosymplectic Manifold ◽  
Conharmonic Curvature Tensor ◽  
Locally Conformal

The aim of the present paper is to study the geometry of locally conformal almost cosymplectic manifold of Φ-holomorphic sectional conharmonic curvature tensor. In particular, the necessaryand sucient conditions in which that locally conformal almost cosymplectic manifold is a manifold of point constant Φ-holomorphic sectional conharmonic curvature tensor have been found. The relation between the mentioned manifold and the Einstein manifold is determined.

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