f-Biharmonic maps and f-biharmonic submanifolds II

• Published in: Journal of mathematical analysis and applications Vol. 455; no. 2; pp. 1285 - 1296
• Main Author: Ou, Ye-Lin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.11.2017
• Subjects: Biharmonic conformal immersions; Biharmonic maps; f-Biharmonic maps; f-Biharmonic submanifolds; Minimal surfaces; f-Biharmonic maps; Biharmonic maps; Minimal surfaces; f-Biharmonic submanifolds; Biharmonic conformal immersions
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2017.06.033

We continue our study [9] 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.