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We prove that the constant maps are the onlyp-harmonic maps for anyp 2 from an arbitrary compact Riemannian manifold into a complete Riemannian manifold which admits a strictly convex function. 相似文献
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In this paper we proved a better estimate as well as generalized to higher codimensions of a theorem of Y.B. Shen on complete submanifolds with parallel mean curvature vector in a hyperbolic space. 相似文献
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We give a complete classification of complete noncompact oriented surfaces with nonnegative Gaussian curvature and finite total mean curvature in R3. 相似文献
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Let M be an n-dimensional complete non-compact submanifold in a hyperbolic space with the norm of its mean curvature vector bounded by
a constant . We prove in this paper that . In particular when M is minimal we have and this is sharp because equality holds when M is totally geodesic.
Received September 14, 1999; in final form November 12, 1999 / Published online December 8, 2000 相似文献
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Pui-Fai Leung 《manuscripta mathematica》1993,79(1):183-185
Leth be the second fundamental form of a compact submanifold of a unit sphere. We show that if ‖h(u, u)‖2<1/3 holds for any unit tangent vectoru at any point on the submanifold then it is a homotopy sphere. 相似文献
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We use the method of H. Gauchman [2] to show that if the sectionalcurvature of a compact minimal n-dimensional submanifold ina unit sphere is everywhere bigger than n/2(n+1) then it mustbe totally geodesic. We also discuss some related results andconjectures. 相似文献
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In this article, we prove that every positively curved, complete non-compact hypersurface in Rn has infinite total mean curvature. 相似文献
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Pui-Fai Leung 《Geometriae Dedicata》1995,56(1):5-6
S. T. Yau proved inAmer. J. Math.
97 (1975), p. 95, Theorem 15 that if the sectional curvature of ann-dimensional compact minimal submanifold in the (n + p)-dimensional unit sphere is everywhere greater than (p – 1)/(2p – 1), then this minimal submanifold is totally geodesic. In this note we improve this bound for the casep 2 to (3p – 2)/(6p). 相似文献
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Pui-Fai Leung 《Annals of Global Analysis and Geometry》1995,13(1):55-58
We prove a sufficient condition for a compact hypersurface in Euclidean space to be spherical in terms of a pinching for the Ricci curvature. 相似文献
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