Contents Online
Communications in Analysis and Geometry
Volume 31 (2023)
Number 5
Submanifolds with constant principal curvatures in symmetric spaces
Pages: 1079 – 1123
DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n5.a2
Authors
Abstract
We study submanifolds whose principal curvatures, counted with multiplicities, do not depend on the normal direction. Such submanifolds, which we briefly call CPC submanifolds, are always austere, hence minimal, and have constant principal curvatures. Well-known classes of examples include totally geodesic submanifolds, homogeneous austere hypersurfaces, and singular orbits of cohomogeneity one actions. The main purpose of this article is to present a systematic approach to the construction and classification of homogeneous submanifolds whose principal curvatures are independent of the normal direction in irreducible Riemannian symmetric spaces of non-compact type and rank
The second author has been supported by projects PID2019-105138GB-C21,MTM2016-75897-P (AEI/FEDER, UE) and ED431C 2019/10, ED431F 2020/04(Xunta de Galicia, Spain).
Received 13 January 2020
Accepted 30 March 2021
Published 16 July 2024