Biharmonic maps into a Riemannian manifold of non-positive curvature

2012/01/31 by Nakauchi, Nobumitsu, Urakawa, Hajime, Gudmundsson, Sigmundur · 2 citations
#53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.6457

Abstract

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.

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• The Second Variational Formula for Statistical Biharmonic Maps
• The second variational formula of the variational problems for mappings between statistical manifolds

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