TY - JOUR AU - Mahi, F. AU - Belkhelfa, M. PY - 2020/06/12 Y2 - 2024/03/29 TI - Legendrian normally flat submanifols of $\mathcal{S}$-space forms: Array JF - Carpathian Mathematical Publications JA - Carpathian Math. Publ. VL - 12 IS - 1 SE - Scientific articles DO - 10.15330/cmp.12.1.69-78 UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/3878 SP - 69-78 AB - <p>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.</p><p>We also prove that if $M$ is Ricci generalized pseudo-parallel, then either it is minimal or $L=\frac{1}{n-1}$, when $c eq -3s$.</p> ER -