Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T23:31:18.352Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1] Bott, R. and Samelson, H., Applications of the theory of Morse to symmetric spaces, Amer. J. Math., 80 (1958), 964–1029.Google Scholar
[2] Chen, B.-Y. and Nagano, T., A Riemannian geometric invariant and its applications to a problem of Borel and Serre, Trans. Amer. Math. Soc, 308 (1988), 273–297.Google Scholar
[3] Loos, O., Charakterisierung symmetrischer R-Räume durch ihre Einheitsgitter, Math. Z., 189 (1985), 211–226.Google Scholar
[4] Takeuchi, M., Cell decompositions and Morse equalities on certain symmetric spaces, J. Fac. Sci. Univ. Tokyo, 12 (1965), 81–192.Google Scholar
[5] Takeuchi, M., On orbits in a compact hermitian symmetric space, Amer. J. Math., 90 (1968), 657–680.CrossRefGoogle Scholar
[6] Takeuchi, M., Basic transformations of symmetric R-spaces, Osaka J. Math., 25 (1988), 259–297.Google Scholar