Some results of F-biharmonic maps

Yingbo Han and Shuxiang Feng

Received: January 10, 2013;   Revised: July 15, 2013;   Accepted: August 26, 2013

Abstract.   In this paper, we give the notion of F-biharmonic maps, which is a generalization of biharmonic maps. We derive the first variation formula which yields F-biharmonic maps. Then we investigate the harmonicity of F-biharmonic maps under the curvature conditions on the target manifold (N, h). We also introduce the stress F-bienergy tensor SF, 2. Then by using the stress F-bienergy tensor SF, 2, we obtain some non existence results of proper F-biharmonic maps under the assumption that SF, 2 = 0. Moreover, we derive some monotonicity formulas for the special case of biharmonic map, i.e. F-biharmonic map with F(t) = t. Then, by using these monotonicity formulas, we obtain new results on the non existence of proper biharmonic isometric immersions from complete manifolds.  

KeywordsF-biharmonic map; stress F-bienergy tensor; harmonic map.  

AMS Subject classification: Primary:  58E20, 53C21 

Version to read:   PDF

Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

Telephone: + 421-2-60295111 Fax: + 421-2-65425882  
e-Mail:    Internet: