| 拟常曲率空间的紧致极小子流形 |
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| 引用本文： | 舒世昌,王迪吉.拟常曲率空间的紧致极小子流形[J].新疆大学学报(理工版),1994,11(4):10-17. |
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| 作者姓名： | 舒世昌 王迪吉 |
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| 作者单位： | 陕西咸阳师专，新疆师范大学 |
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| 摘 要： | 通过揭示拟常曲率空间中紧致极小子流形Ｍ的内在量Ｋ、Ｑ和Ｒ之间的关系，给出拟常曲率空间紧致极小子流形是全测地子流形的几个充分条件．推广和包含了常曲率空间中Ｓ．Ｔ．Ｙａｕ的一个相应结果．
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| 关 键 词： | 截面曲率 李齐曲率 拟常曲率空间 |
Minimal Submanifolds in A Riemannian Manifold of Quasi Constant Curvature |
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| Shu Shichang, Wang Diji.Minimal Submanifolds in A Riemannian Manifold of Quasi Constant Curvature[J].Journal of Xinjiang University(Science & Engineering),1994,11(4):10-17. |
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| Authors: | Shu Shichang Wang Diji |
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| Institution: | Shu Shichang; Wang Diji(Xianyang Teachers' Collage)(Xinjiang Normal University) |
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| Abstract: | Let M be an n-dimensional compact minimal submanifold in a Riemannian manifold V+, of quasi constant curvature,Let K and Q be the infinimum of the Sectional curvature and Ricci Curvature of M respectively. Let R be the Scalar curvature of M,in this paper,we obtain some relations of K,Q and R,give some sufficient conditions for a compact minimal submanifold in Vn+p to be totally geodesic submanifold. In particular, when Vn+p is a manifold of constant curvature. i. e. b= 0,we obtain the same result of S. T. Yau's Theorem. |
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| Keywords: | Quasi coustant curvature sectional curvature Ricci curvature Scalar curvature |
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