| 常曲率黎曼流形中具平行平均曲率向量的二维浸入曲面 |
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| 引用本文： | 王宝富. 常曲率黎曼流形中具平行平均曲率向量的二维浸入曲面[J]. 四川大学学报(自然科学版), 1993, 30(3): 305-313 |
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| 作者姓名： | 王宝富 |
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| 作者单位： | 四川大学数学系 |
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| 摘 要： | 构造了常曲率黎曼流形中具平行平均曲率向量的二维浸入曲面上的全纯微分形式,在同胚球时,给出了其上的Frenet-Boruvka公式及维数定理;估计了浸入的高斯曲率及像的面积;并研究了该浸入的Pinching问题.
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| 关 键 词： | 同胚球 黎曼流形 平均曲率向量 |
2-IMMERSION SURFACE WITH PARALLEL MEAN CURVATURE VECTOR IN RIEMANN MANIFOLD OF CONSTANT CURVATURE |
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| Wang Baofu. 2-IMMERSION SURFACE WITH PARALLEL MEAN CURVATURE VECTOR IN RIEMANN MANIFOLD OF CONSTANT CURVATURE[J]. Journal of Sichuan University (Natural Science Edition), 1993, 30(3): 305-313 |
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| Authors: | Wang Baofu |
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| Affiliation: | Department of mathematics |
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| Abstract: | We construct some holomorphic forms on the 2- immersion surface with parallel mean curvature vector in Riemann manifold of constant curvature. In the case of homeomorphic sphere, we obtain the Frenet-Boruvka formula and a dimension theorem, and estimate the Gauss curvature and the image area. Finally,we study the Pinching problem of the immersion. |
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| Keywords: | humeomorphie sphere Rie-Roch theorem osculating space. |
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