Two-number of symmetric R-spaces
Two-number of symmetric R-spaces
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两个对称 R 空间
DOI：
10.1017/s0027763000001513
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发表时间：
1989
影响因子：
0.8
通讯作者：
M. Takeuchi
中科院分区：
文献类型：
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作者：
M. Takeuchi
Chen-Nagano [2]对紧致（连通）对称空间M引入了一个黎曼几何不变量v（M），称为2-数：称点p，q <$M彼此对映，如果p = q或存在M的一条闭测地线，其中p和q彼此对映。M的子集A称为对极子集，如果A的每一对点彼此对极。现在2-数v（M）被定义为最大可能基数|一|M的对映子集A。2-数是有限的。
Chen-Nagano [2] introduced a Riemannian geometric invariant v(M), called the 2-number, for a compact (connected) symmetric space M: Points p, q ∊ M are said to be antipodal to each other, if p = q or there is a closed geodesic of M on which p and q are antipodal to each other. A subset A of M is called an antipodal subset if every pair of points of A are antipodal to each other. Now the 2-number v(M) is defined as the maximum possible cardinality |A| of an antipodal subset A of M. The 2-number is finite.