F-Harmonic Maps between Doubly Warped Product Manifolds

Abstract

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.

Classification of Warped Product Submanifolds in Kenmotsu Space Forms Admitting Gradient Ricci Solitons

“…It is also called the fundamental equation of Ricci tensor in terms of Hessian tensor. For the gradient, Ricci soliton can be classified as: Gradient Ricci solitons are extensively studied and a few results on classifications of gradient Ricci soliton and some of them with warped product structures have been studied in [13][14][15][16][17][18][19][20][21][22][23]. Our aim of this paper to find the classification of derived inequality (1) attaining the equality cases by using the tool of gradient Ricci solitons, in terms of the squared norm of second fundamental form and constant sectional curvature.…”

Stability of λ-Harmonic Maps

“…In view of physics, harmonic maps have been studied in various fields of physics, such as super conductor, ferromagnetic material, liquid crystal, etc. [1][2][3][4][5][6][7][8][9].…”

“…For instance, instead of the scalar field in the Lagrangian, some of the F -harmonic maps, such as the trigonometric functions, are studied in order to reproduce the inflation. Moreover, there are other F -harmonic maps, such as exponential harmonic maps, are investigated in order to depict the phenomenon of the quintessence [5,29,30].…”