Legendrian normally flat submanifols of $\mathcal{S}$-space forms

  • F. Mahi Department of Exact Sciences, Ecole Normale Supérieure de Mostaganem, Mostaganem 27000, Algeria
  • M. Belkhelfa Laboratoire de Physique Quantique de la Matière et Modélisations Mathématiques, Faculty of Exact Sciences, Mustapha Stambouli University, Mascara 29000, Algeria https://orcid.org/0000-0002-2570-6742
Keywords: $\mathcal{S}$-space form, Legendrian submanifold, normally flat submanifold, pseudo-parallel submanifold, Ricci generalized pseudo-parallel submanifold
Published online: 2020-06-12

Abstract


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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How to Cite
(1)
Mahi F., Belkhelfa M. Legendrian Normally Flat Submanifols of $\mathcal{S}$-Space Forms. Carpathian Math. Publ. 2020, 12 (1), 69-78.