Sequences of Maximal Antipodal Sets of Oriented Real Grassmann Manifolds II

  • Hiroyuki TasakiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 203)


Chen–Nagano introduced the notion of antipodal sets of compact Riemannian symmetric spaces. The author showed a correspondence between maximal antipodal sets of oriented real Grassmann manifolds and certain families of subsets of finite sets and reduced the classifications of maximal antipodal sets of oriented real Grassmann manifolds to a certain combinatorial problem in a previous paper. In this paper we construct new sequences of maximal antipodal sets from those obtained in previous papers and estimate the cardinalities of antipodal sets.



The author was partly supported by the Grant-in-Aid for Science Research (C) (No. 15K04835), Japan Society for the Promotion of Science.


  1. 1.
    Chen, B.-Y., Nagano, T.: A Riemannian geometric invariant and its applications to a problem of Borel and Serre. Trans. Amer. Math. Soc. 308, 273–297 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Frankl, P., Tokushige, N.: Uniform eventown problems. Eur. J. Comb. 51, 280–286 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Tasaki, H.: Antipodal sets in oriented real Grassmann manifolds, Int. J. Math. 24(8), Article ID: 1350061, 1–28 (2013)Google Scholar
  4. 4.
    Tasaki, H.: Sequences of maximal antipodal sets of oriented real Grassmann manifolds, In: Suh, Y.J., et al. (eds.) ICM Satellite Conference on “Real and Complex Submanifolds”, Springer Proceedings in Mathematics and Statistics, vol. 106, pp. 515–524 (2014)Google Scholar
  5. 5.
    Tasaki, H.: Estimates of antipodal sets in oriented real Grassmann manifolds, “Global Analysis and Differential Geometry on Manifolds”. Int. J. Math. 26(5), Article ID: 1541008, 1–12 (2015). (special issue: the Kobayashi memorial volume)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Division of Mathematics, Faculty of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan

Personalised recommendations