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

• Published in: Annals of global analysis and geometry Vol. 54; no. 2; pp. 173 - 185
• Main Authors: Carriazo, Alfonso, Martín-Molina, Verónica, Vrancken, Luc
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2018; Springer Nature B.V; Springer Verlag
• Subjects: Analysis; Differential Geometry; Geometry; Global Analysis and Analysis on Manifolds; Manifolds (mathematics); Mathematical Physics; Mathematics; Mathematics and Statistics; Legendrian submanifold; 53C40; Totally geodesic; Totally umbilical; 53C15; 53C25; space; totally geodesic; κ-space µ; totally umbilical

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.