Biharmonic maps into a Riemannian manifold of non-positive curvature
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We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions.
KeywordsHarmonic map Biharmonic map Chen’s conjecture Generalized Chen’s conjecture
Mathematics Subject Classification (2000)Primary 58E20 Secondary 53C43
The second author would like to express his sincere gratitude to Professor Sigmundur Gudmundsson for his hospitality and very intensive and helpful discussions during for the second author staying at Lund University, at 2012 May. Addition of part of Section Three to the original version of the first and second authors was based by this joint work with him during this period.
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