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
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