A canonical distribution on isoparametric submanifolds I

• Autores: Cristián U. Sánchez
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 1, 2020, págs. 113-130
• Idioma: inglés
• DOI: 10.33044/revuma.v61n1a07
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• Resumen

  • We show that on every compact, connected homogeneous isoparametric submanifold M of codimension h≥2 in a Euclidean space, there exists a canonical distribution which is bracket generating of step 2. An interesting consequence of this fact is also indicated. In this first part we consider only the case in which the system of restricted roots is reduced, reserving for a second part the case of non-reduced restricted roots.

• Referencias bibliográficas
  • Berndt, J., Console, S., Olmos, C. Submanifolds and Holonomy. Second edition. CRC Press, Boca Raton, 2016. MR 3468790.
  • Freudenthal, H., de Vries, H. Linear Lie Groups. Academic Press, New York and London, 1969. MR 0260926.
  • Heintze, E., Olmos, C., Thorbergsson, G. Submanifolds with constant principal curvatures and normal holonomy groups. Internat. J. Math. 2...
  • Helgason S. Differential Geometry, Lie Groups and Symmetric Spaces. Academic Press, New York and London, 1978. MR 0514561.
  • Kammeyer, H. An explicit rational structure for real semisimple Lie algebras. J. Lie Theory 24 (2014), no. 2, 307–319. MR 3235892.
  • Knapp, A. Lie Groups Beyond an Introduction. Second edition. Birkh¨auser, Boston, 2002. MR 192038
  • Thorbergsson, G. Isoparametric foliations and their buildings. Ann. Math. (2) 133 (1991), no. 2, 429–446. MR 1097244.
  • Warner, G. Foundation of Differentiable Manifolds and Lie Groups. Scott, Foresman and Co. Glenview, Ill.-London, 1971. MR 0295244.