scholarly journals Existence of some classes of N(k)-quasi Einstein manifolds

2021 ◽  
Vol 39 (5) ◽  
pp. 145-162
Author(s):  
Sudhakar Kumar Chaubey ◽  
K. K. Bhaishya ◽  
M. Danish Siddiqi
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Unit Vector ◽  
Characteristic Vector ◽  
Einstein Manifolds ◽  
Unit Vector Fields ◽  
Characteristic Vector Field

The object of the present paper is to study some classes of N(k)-quasi Einstein manifolds. The existence of such manifolds are proved by giving non-trivial physical and geometrical examples. It is also proved that the characteristic vector field of the manifold is killing as well as parallel unit vector fields under certain curvaturerestrictions.

scholarly journals On Generalized ϕ-Recurrent (ϵ,δ)-Trans-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
C. S. Bagewadi ◽  
Dakshayani A. Patil
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Characteristic Vector ◽  
Sasakian Manifolds ◽  
Characteristic Vector Field

We study generalized ϕ-recurrent (ϵ,δ)-trans-Sasakian manifolds. A relation between the associated 1-forms A and B and relation between characteristic vector field ξ and the vector fields ρ1, ρ2 for a generalized ϕ-recurrent.

scholarly journals Harmonic characteristic vector fields on contact metric three-manifolds

2003 ◽  
Vol 67 (2) ◽  
pp. 305-315 ◽  
Author(s):  
Domenico Perrone
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Harmonic Map ◽  
Characteristic Vector ◽  
Dense Open Subset ◽  
Sphere Bundle ◽  
Sasaki Metric ◽  
Characteristic Vector Field ◽  
Characteristic Vector Fields ◽  
Unit Tangent Sphere Bundle

In this paper we show that a contact metric three-manifold is a generalised (k, μ)-space on an everywhere dense open subset if and only if its characteristic vector field ξ determines a harmonic map from the manifold into its unit tangent sphere bundle equipped with the Sasaki metric. Moreover, we classify the contact metric three-manifolds whose characteristic vector field ξ is strongly normal (or equivalently, is harmonic and minimal).

scholarly journals Harmonic and minimal unit vector fields on Riemannian symmetric spaces

2003 ◽  
Vol 47 (4) ◽  
pp. 1273-1286 ◽  
Author(s):  
Jürgen Berndt ◽  
Lieven Vanhecke ◽  
László Verhóczki
Keyword(s):  
Symmetric Spaces ◽  
Vector Fields ◽  
Unit Vector ◽  
Unit Vector Fields ◽  
Riemannian Symmetric Spaces

scholarly journals Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 179-186
Author(s):  
Sharief Deshmukh ◽  
Uday De ◽  
Peibiao Zhao
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field ? belonging to the (k,?)'-nullity distribution and (k,?)-nullity distribution respectively. Finally, an illustrative example is given.

scholarly journals Poincaré index and the volume functional of unit vector fields on punctured spheres

2019 ◽  
Vol 161 (3-4) ◽  
pp. 487-499
Author(s):  
Fabiano G. B. Brito ◽  
André O. Gomes ◽  
Icaro Gonçalves
Keyword(s):  
Vector Fields ◽  
Unit Vector ◽  
Volume Functional ◽  
Poincaré Index ◽  
Unit Vector Fields ◽  
Poincare Index

Invariant harmonic unit vector fields on the oscillator groups

2019 ◽  
Vol 69 (4) ◽  
pp. 907-924
Author(s):  
Na Xu ◽  
Ju Tan
Keyword(s):  
Vector Fields ◽  
Unit Vector ◽  
Unit Vector Fields
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