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Two-number of symmetric R-spaces

Published online by Cambridge University Press:  22 January 2016

Masaru Takeuchi
Masaru Takeuchi*
Affiliation:
Department of Mathematics, College of General Education, Osaka University, Toyonaka 560, Japan
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 43 - 46
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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