A classification of totally geodesic and totally umbilical Legendrian submanifolds of $$(\kappa ,\mu )$$-spaces |
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| Authors: | Alfonso Carriazo Verónica Martín-Molina Luc Vrancken |
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| Institution: | 1.Departamento de Geometría y Topología, Facultad de Matemáticas,Universidad de Sevilla,Seville,Spain;2.Departamento de Didáctica de las Matemáticas, Facultad de Ciencias de la Educación,Universidad de Sevilla,Seville,Spain;3.LAMAV,Université de Valenciennes,Valenciennes Cedex 9,France;4.Departement Wiskunde,KU Leuven,Leuven,Belgium |
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| 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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