Abstract
We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of \((\kappa ,\mu )\)-spaces with Boeckx invariant \(I \le -1\). In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.
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The first two authors are partially supported by the MINECO-FEDER Grant MTM2014-52197-P. They are members of the IMUS (Instituto de Matemáticas de la Universidad de Sevilla), and of the PAIDI groups FQM-327 and FQM-226 (Junta de Andalucía, Spain), respectively.
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Carriazo, A., Martín-Molina, V. & Vrancken, L. A classification of totally geodesic and totally umbilical Legendrian submanifolds of \((\kappa ,\mu )\)-spaces. Ann Glob Anal Geom 54, 173–185 (2018). https://doi.org/10.1007/s10455-018-9597-1
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DOI: https://doi.org/10.1007/s10455-018-9597-1