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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).
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참고문헌 (25)
참고문헌 신청
A. Balmus / 2010 / Biharmonic hypersurfaces in 4-dimensional space form / Math. Nachr 283 (12) : 1696 ~ 1705
B. Y. Chen / 1988 / Some open problems and conjectures on submanifolds of finite type / Michigan State University
C. Oniciuc / 2002 / Biharmonic maps between Riemannian manifolds / An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 48 (2) : 237 ~ 248
C. Wang / 2004 / Biharmonic maps from R4 into Riemannian manifold / Math. Z 247 (1) : 65 ~ 87
C. Wang / 2004 / Remarks on biharmonic maps into spheres / Calc. Var. Partial Differential Equations 21 (3) : 221 ~ 242
B. Y. Chen / 1988 / Some open problems and conjectures on submanifolds of finite type / Michigan State University
C. Oniciuc / 2002 / Biharmonic maps between Riemannian manifolds / An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 48 (2) : 237 ~ 248
C. Wang / 2004 / Biharmonic maps from R4 into Riemannian manifold / Math. Z 247 (1) : 65 ~ 87
C. Wang / 2004 / Remarks on biharmonic maps into spheres / Calc. Var. Partial Differential Equations 21 (3) : 221 ~ 242
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