SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD

- Journal title : Journal of the Korean Mathematical Society
- Volume 52, Issue 5, 2015, pp.1097-1108
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2015.52.5.1097

Title & Authors

SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD

HAN, YINGBO; ZHANG, WEI;

HAN, YINGBO; ZHANG, WEI;

Abstract

In this paper, we investigate p-biharmonic maps u : (M, g) (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature. We obtain that if < and < , then u is harmonic, where is a nonnegative constant and . We also obtain that any weakly convex p-biharmonic hypersurfaces in space formN(c) with is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen`s conjecture for p-biharmonic submanifolds).

Keywords

p-biharmonic maps;p-biharmoinc submanifolds;

Language

English

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