Submanifold geometry in symmetric spaces of noncompact type

In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar and hyperpolar actions, and homogeneous CPC submanifolds.

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Bibliographic Details
Published in:São Paulo Journal of Mathematical Sciences 2021-06, Vol.15 (1), p.75-110
Main Authors: Díaz-Ramos, J. Carlos, Domínguez-Vázquez, Miguel, Sanmartín-López, Víctor
Format: Article
Language:English
Subjects:
Hyperspaces
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Special Section: An Homage to Manfredo P. do Carmo
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Summary:In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar and hyperpolar actions, and homogeneous CPC submanifolds.
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-019-00119-6