Abstract
In this paper, some properties of F -harmonic and conformal F -harmonic maps between doubly warped product manifolds are studied and new examples of non-harmonic F -harmonic maps are constructed.
Highlights
Let φ : ( M, g) → ( N, h) be a smooth map between Riemannian manifolds
The map φ is called harmonic if it is a critical point of the energy functional: E(φ) =
The Euler–Lagrange equation corresponding to the energy functional is given by vanishing of the tension field τ (φ) := trace g ∇dφ
Summary
Let φ : ( M, g) → ( N, h) be a smooth map between Riemannian manifolds. The map φ is called harmonic if it is a critical point of the energy functional: E(φ) = Z K e(φ)dυg (1)for any compact sub-domain K ⊆ M, where e(φ) := 12 | dφ |2 is the energy density of φ. In this paper, following the ideas in [31], F -harmonic and conformally F -harmonic maps between doubly warped product manifolds are studied. M × N and doubly warped product manifold M μ ×λ N is given as follows: Theorem 1.
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