Legendrian normally flat submanifols of $\mathcal{S}$-space forms
Array
DOI:
https://doi.org/10.15330/cmp.12.1.69-78Keywords:
$\mathcal{S}$-space form, Legendrian submanifold, normally flat submanifold, pseudo-parallel submanifold, Ricci generalized pseudo-parallel submanifoldAbstract
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 $c\neq -3s$.
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Published
2020-06-12
How to Cite
(1)
Mahi, . F.; Belkhelfa, M. Legendrian Normally Flat Submanifols of $\mathcal{S}$-Space Forms: Array. Carpathian Math. Publ. 2020, 12, 69-78.
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Scientific articles