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2000•Journal of Anhui Normal UniversityRequires access

CLOSED SUBMANIFOLDS WITH NON ZERO PARALLEL MEAN CURVATURE VECTOR IN UNIT SPHERE S~(n+p)(1)(p>1)

Wang Ru

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Abstract

In this paper, by using the method in [1], the closed submanifolds with non zero parallel mean curveture vector in unit sphere is studied. We find the closed submonifolds is a small sphere, Clifford torus, H(r) torus or Veronese surface under certain condition of the square of the length of the second foundamental form and the mean curvature, which improved the result in [3]. Also in the case n=2, we give the characterization of a class of surfaces with Gauss curvature K=0, 13(H 2+1), which developed the results in [7].

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What this paper is about

In this paper, by using the method in [1], the closed submanifolds with non zero parallel mean curveture vector in unit sphere is studied. We find the closed submonifolds is a small sphere, Clifford torus, H(r) torus or Veronese surface under certain condition of the square of the length of the second foundamental form and the mean curvature, which improved the result in [3]. Also in the case n=2, we give the characterization of a class of surfaces with Gauss curvature K=0, 13(H 2+1), which developed the results in [7].

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Available abstract

In this paper, by using the method in [1], the closed submanifolds with non zero parallel mean curveture vector in unit sphere is studied. We find the closed submonifolds is a small sphere, Clifford torus, H(r) torus or Veronese surface under certain condition of the square of the length of the second foundamental form and the mean curvature, which improved the result in [3]. Also in the case n=2, we give the characterization of a class of surfaces with Gauss curvature K=0, 13(H 2+1), which developed the results in [7].

Key concepts: Mean curvature, Torus, Mathematics, Zero (linguistics), Unit sphere, Gaussian curvature, Curvature, Surface (topology)

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