A classification of totally geodesic and totally umbilical Legendrian submanifolds of (κ,μ)-spaces

Alfonso Carriazo (1) , Veronica Martin-Molina (1) , Luc Vrancken (2, 3, 4)

1 Universidad de Sevilla = University of Seville
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015
3 KU Leuven - Technologie campus Gent - KU Leuven
4 INSA Hauts-De-France - INSA Institut National des Sciences Appliquées Hauts-de-France

We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of (κ,μ)-spaces with Boeckx invariant I≤−1. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct

Mots clés: (κ-space µ); Legendrian submanifold; totally geodesic; totally umbilical

Domaines: Géométrie différentielle [math.DG]

Alfonso Carriazo, Veronica Martin-Molina, Luc Vrancken. A classification of totally geodesic and totally umbilical Legendrian submanifolds of (κ,μ)-spaces. Annals of Global Analysis and Geometry, 2018, 54 (2), pp.173-185. ⟨10.1007/s10455-018-9597-1⟩. ⟨hal-03722206⟩