Some results of
F-biharmonic mapsYingbo 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 S_{F,}_{ 2}. Then
by using the stress F-bienergy tensor S_{F,}_{ 2},
we obtain some non existence results of proper F-biharmonic maps under the
assumption that S_{F,}_{ 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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