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

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.

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Bibliographic Details
Published inAnnals of global analysis and geometry Vol. 54; no. 2; pp. 173 - 185
Main Authors Carriazo, Alfonso, Martín-Molina, Verónica, Vrancken, Luc
Format Journal Article
LanguageEnglish
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
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Summary: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.
ISSN:0232-704X
1572-9060
DOI:10.1007/s10455-018-9597-1