ﻻ يوجد ملخص باللغة العربية
We continue our study [Ou4] of f-biharmonic maps and f-biharmonic submanifolds by exploring the applications of f-biharmonic maps and the relationships among biharmonicity, f-biharmonicity and conformality of maps between Riemannian manifolds. We are able to characterize harmonic maps and minimal submanifolds by using the concept of f-biharmonic maps and prove that the set of all f-biharmonic maps from 2-dimensional domain is invariant under the conformal change of the metric on the domain. We give an improved equation for f-biharmonic hypersurfaces and use it to prove some rigidity theorems about f-biharmonic hypersurfaces in nonpositively curved manifolds, and to give some classifications of f-biharmonic hypersurfaces in Einstein spaces and in space forms. Finally, we also use the improved f-biharmonic hypersurface equation to obtain an improved equation and some classifications of biharmonic conformal immersions of surfaces into a 3-manifold.
In this paper, we prove that the class of bi-f-harmonic maps and that of f-biharmonic maps from a conformal manifold of dimension not equal to 2 are the same (Theorem 1.1). We also give several results on nonexistence of proper bi-f-harmonic maps and
In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pse
We study biharmonic hypersurfaces and biharmonic submanifolds in a Riemannian manifold. One of interesting problems in this direction is Chens conjecture which says that any biharmonic submanifold in a Euclidean space is minimal. From the invariant e
This note reviews some of the recent work on biharmonic conformal maps (see cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same dimension and
Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to sev