In this paper, we introduce the Mus-Sasaki metric on the tangent bundle T M , as a new natural metric on T M. We establish necessary and sufficient conditions under which a vector field is harmonic with respect to the Mus-Sasaki metric. We also construct some examples of harmonic vector fields.
In this paper, we extend the definition of F-harmonic maps [1] and, we give the notion of F-biharmonic maps, which is a generalization of biharmonic maps between Riemannian manifolds [3] and f-biharmonic maps [7] and we discuss some conformal properties and the stability of F-harmonic maps. Also, we give a formula to construct some examples of proper Fbiharmonic maps. Our results are extensions of [1] and [7].
This paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a
deformation non-conform of Sasaki metric over an n-dimensional Riemannian
manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric
and we characterize a new class of proper biharmonic maps. Examples of proper
biharmonic maps are constructed when all of the factors are Euclidean spaces.
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.
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