Open AccessLegendrian normally flat submanifols of $\mathcal{S}$-space forms
Author(s) -
F.T. Mahi,
Mohamed Belkhelfa
Publication year - 2020
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.12.1.69-78
Subject(s) - mathematics , submanifold , geodesic , space (punctuation) , totally geodesic , constant (computer programming) , combinatorics , constant curvature , sectional curvature , curvature , pure mathematics , mathematical analysis , geometry , scalar curvature , philosophy , linguistics , computer science , programming language
In the present study, we consider a Legendrian normally flat submanifold $M$ of $(2n+s)$-dimensional $\mathcal{S}$-space form $\widetilde{M}^{2n+s}(c)$ of constant $\varphi$-sectional curvature $c$. We have shown that if $M$ is pseudo-parallel then $M$ is semi-parallel or totally geodesic.
We also prove that if $M$ is Ricci generalized pseudo-parallel, then either it is minimal or $L=\frac{1}{n-1}$, when $c\neq -3s$.