Biharmonic maps into a Riemannian manifold of non-positive curvature

By Nobumitsu Nakauchi, Hajime Urakawa, Sigmundur Gudmundsson. Geometry of Biharmonic Mappings, 2012

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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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e40dc3be47e1de481e2ecb42a83105c7fb587ba5