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.
The goal of this work is the application of the f-stress energy of differ-ential forms to study the generalized monotonicity formulae and generalizedvanishing theorems. We obtain some generalized monotonicity formulas forp-formsω∈Ap(ξ), which satisfy the generalizedf-conservation laws, withf∈C∞(M×R) satisfying some conditions
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