| 伪欧氏空间的伪球面子流形 |
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| 引用本文： | 潘兴侠,欧阳崇珍.伪欧氏空间的伪球面子流形[J].南昌大学学报(理科版),2005,29(3):211-214. |
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| 作者姓名： | 潘兴侠 欧阳崇珍 |
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| 作者单位： | 南昌大学,数学系,江西,南昌,330047 |
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| 基金项目： | 国家自然科学基金资助项目(10261006)，教育部优秀博士论文专项基金资助项目(200217)，江西省自然科学基金资助项目(0211005) |
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| 摘 要： | 将子流形的位置向量分解成水平分量和垂直分量，运用活动标架法研究伪欧氏空间的伪球面子流形。得到紧致类空子流形是伪球面子流形的两个充要条件：1)子流形的支撑函数是常值函数；2)子流形位置向量的水平分量是调和的。同时，给出具有平行平均曲率向量场的子流形是伪球面子流形的一个充要条件。特别地，对于Chen子流形，若它具有非迷向的平行平均曲率向量场且其支撑函数有固定符号，则它是伪球面子流形。
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| 关 键 词： | 类空子流形 伪球面子流形 Chen子流形 平行平均曲率向量场 |
| 文章编号： | 1006-0464(2005)03-0211-04 |
| 修稿时间： | 2004年7月15日 |
PSEUDO-SPHERICAL SUBMANIFOLDS OF PSEUDO-EUCLIDEAN SPACE |
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| PAN Xing-xia,OUYANG Chong-zhen.PSEUDO-SPHERICAL SUBMANIFOLDS OF PSEUDO-EUCLIDEAN SPACE[J].Journal of Nanchang University(Natural Science),2005,29(3):211-214. |
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| Authors: | PAN Xing-xia OUYANG Chong-zhen |
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| Abstract: | Decomposing the position vectors of a submanifold into the tangential and normal components,the present paper studies the conditions under which a compact space-like submanifold of pseudo-Euclidean space is pseudo-spherical submanifold.It is observed that the tangential components of the position vectors being harmonic and the support function of the submanifold being contant provides two necessary and sufficient conditions.At the same time,we obtain another necessary and sufficient condition for the submanifold with parallel mean curvature vector.Specially,we also study Chen submanifold and obtain that if its mean curvature vector is parallel and not isotropic and the support function doesn't chang its sign,it is pseudo-spherical submanifold. |
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| Keywords: | space-like submanifold pseudo-spherical submanifold Chen submanifold parallel mean curvature vector |
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