2007
DOI: 10.1007/s00209-007-0236-y
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The stress-energy tensor for biharmonic maps

Abstract: Using Hilbert’s criterion, we consider the stress-energy tensor associated to the bienergy functional. We show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four. First, we use this tensor to construct new exam- ples of biharmonic maps, then classify maps with vanishing or parallel stress-energy tensor and Riemannian immersions whose stress-energy tensor is proportional to the metric, thus obtaining a weaker but high-dimensional version of the Hopf Theorem on co… Show more

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Cited by 58 publications
(67 citation statements)
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“…Various forms of the above result were obtained in [7,17,23]. From here we deduce some characterization formulas for the biconservativity.…”
Section: Biconservative Submanifolds; General Propertiesmentioning
confidence: 61%
“…Various forms of the above result were obtained in [7,17,23]. From here we deduce some characterization formulas for the biconservativity.…”
Section: Biconservative Submanifolds; General Propertiesmentioning
confidence: 61%
“…It was proved in [44] that the critical points of this new functional are given by the vanishing of the stress-bienergy tensor Furthermore, interesting relations between the stress-bienergy tensor of a submanifold in the Euclidean space and its associated Gauss map were proved.…”
Section: Corollary ([42]) the Biharmonic Map Derived From The Generamentioning
confidence: 99%
“…The stress bi-energy tensor was also studied in [7] and those results could be useful when we study conformal maps. The stress bi-energy tensor of φ satisfies the following relationship divS 2 (φ) = h (τ 2 (φ), dφ) .…”
Section: Introductionmentioning
confidence: 99%