A property of homogeneous isoparametric submanifolds

• Cristián U. Sánchez ^[1]
  1. [1] Universidad Nacional de C´ordoba, C´ordoba, Argentina
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 269-279
• Idioma: inglés
• DOI: 10.33044/revuma.4941
• Enlaces
  • Texto completo
• Resumen

  • The present paper contains a new result concerning the second fundamental form of a compact, connected, homogeneous, isoparametric submanifold of codimension h≥2 in a Euclidean space.

• Referencias bibliográficas
  • .Agrachev, D. Barilari, and U. Boscain, A comprehensive introduction to sub-Riemannian geometry, Cambridge Stud. Adv. Math. 181, Cambridge...
  • A. A. Agrachev and A. V. Sarychev, Sub-Riemannian metrics: Minimality of abnormal geodesics versus subanalyticity, ESAIM Control Optim. Calc....
  • J. Berndt, S. Console, and C. Olmos, Submanifolds and holonomy, second ed., Monogr. Res. Notes Math., CRC Press, Boca Raton, FL, 2016. DOI...
  • M. Gromov, Carnot–Carathéodory spaces seen from within, in Sub-Riemannian geometry, Progr. Math. 144, Birkhäuser, Basel, 1996, pp. 79–323....
  • E. Hakavuori, Sub-Riemannian geodesics, Ph.D. thesis, University of Jyväskylä, 2019. Available at https://urn.fi/URN:ISBN:978-951-39-7810-5.
  • S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure Appl. Math. 80, Academic Press, New York-London, 1978. MR Zbl
  • R. Montgomery, Survey of singular geodesics, in Sub-Riemannian geometry, Progr. Math. 144, Birkhäuser, Basel, 1996, pp. 325–339. MR Zbl
  • R. Montgomery, A tour of subriemannian geometries, their geodesics and applications, Math. Surveys Monogr. 91, American Mathematical Society,...
  • R. Monti, The regularity problem for sub-Riemannian geodesics, in Geometric control theory and sub-Riemannian geometry, Springer INdAM Ser....
  • C. Olmos and C. Sánchez, A geometric characterization of the orbits of s-representations, J. Reine Angew. Math. 420 (1991), 195–202. DOI...
  • R. S. Palais and C.-L. Terng, A general theory of canonical forms, Trans. Amer. Math. Soc. 300 no. 2 (1987), 771–789. DOI MR Zbl
  • C. U. Sánchez, A canonical distribution on isoparametric submanifolds I, Rev. Un. Mat. Argentina 61 no. 1 (2020), 113–130. DOI MR Zbl
  • C. U. Sánchez, A canonical distribution on isoparametric submanifolds II, Rev. Un. Mat. Argentina 62 no. 2 (2021), 491–513. DOI MR Zbl
  • G. Thorbergsson, Isoparametric foliations and their buildings, Ann. of Math. (2) 133 no. 2 (1991), 429–446. DOI MR Zbl
  • G. Thorbergsson, A survey on isoparametric hypersurfaces and their generalizations, in Handbook of differential geometry. Vol. I, North-Holland,...
  • G. Thorbergsson, From isoparametric submanifolds to polar foliations, São Paulo J. Math. Sci. 16 no. 1 (2022), 459–472. DOI MR Zbl
  • F. W. Warner, Foundations of differentiable manifolds and Lie groups, Scott, Foresman, and Co., Glenview, Ill.-London, 1971. MR Zbl