On annihilators of harmonic vector fields

1998 ◽  
Vol 92 (1) ◽  
pp. 3600-3612
Author(s):  
B. Gustafsson ◽  
D. Khavinson
Keyword(s):  
Vector Fields ◽  
Harmonic Vector ◽  
Harmonic Vector Fields

Twisted Sasakian Metric on the Tangent Bundle and Harmonicity

2021 ◽  
Vol 62 ◽  
pp. 53-66
Author(s):  
Fethi Latti ◽  
◽  
Hichem Elhendi ◽  
Lakehal Belarbi
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Sufficient Conditions ◽  
Harmonic Vector ◽  
New Class ◽  
Necessary And Sufficient ◽  
Sasakian Metric ◽  
Harmonic Vector Fields

In the present paper, we introduce a new class of natural metrics on the tangent bundle $TM$ of the Riemannian manifold $(M,g)$ denoted by $G^{f,h}$ which is named a twisted Sasakian metric. A necessary and sufficient conditions under which a vector field is harmonic with respect to the twisted Sasakian metric are established. Some examples of harmonic vector fields are presented as well.

scholarly journals SOME VECTORS FIELDS ON THE TANGENT BUNDLE WITH A SEMI-SYMMETRIC METRIC CONNECTION

2021 ◽  
pp. 669
Author(s):  
Aydin Gezer ◽  
Erkan Karakas
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Harmonic Vector ◽  
Metric Connection ◽  
Projective Vector ◽  
Harmonic Vector Fields

Let $M$ is a (pseudo-)Riemannian manifold and $TM$ be its tangent bundlewith the semi-symmetric metric connection $\overline{\nabla }$. In thispaper, we examine some special vector fields, such as incompressible vectorfields, harmonic vector fields, concurrent vector fields, conformal vectorfields and projective vector fields on $TM$ with respect to thesemi-symmetric metric connection $\overline{\nabla }$ and obtain someproperties related to them.

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