p. 47 - 66 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. Keywords: F-biharmonic map; stress F-bienergy tensor; harmonic map. AMS Subject classification: Primary: 58E20, 53C21 PDF Compressed Postscript Version to read 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: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2014, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |