SOME RESULTS OF p-BIHARMONIC MAPS INTO A NON-POSITIVELY CURVED MANIFOLD
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In this paper, we investigate p-biharmonic maps u : (M, g) → (N, h) from a Riemannian manifold into a Riemannian manifold with nonpositive sectional curvature. We obtain that if ∫M |τ(u)|a+pdvg < ∞ and ∫M |d(u)|2dvg < ∞, then u is harmonic, where a ≥ 0 is a nonnegative constant and p ≥ 2. We also obtain that any weakly convex p-biharmonic hypersurfaces in space form N(c) with c ≤ 0 is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen’s conjecture for p-biharmonic submanifolds).
Abstract
In this paper, we investigate p-biharmonic maps u : (M, g) → (N, h) from a Riemannian manifold into a Riemannian manifold with nonpositive sectional curvature. We obtain that if ∫M |τ(u)|a+pdvg < ∞ and ∫M |d(u)|2dvg < ∞, then u is harmonic, where a ≥ 0 is a nonnegative constant and p ≥ 2. We also obtain that any weakly convex p-biharmonic hypersurfaces in space form N(c) with c ≤ 0 is minimal. These results give affirmative partial answer to Conjecture 2 (generalized Chen’s conjecture for p-biharmonic submanifolds).
참고문헌 (25)
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