Legendrian normally flat submanifols of S-space forms

Authors

  • 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
https://doi.org/10.15330/cmp.12.1.69-78

Keywords:

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 S-space form ˜M2n+s(c) of constant φ-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=1n1, when c3s.

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