Geodesic
On normal CR-submanifolds of S-manifolds
Colloquium Mathematicum, Tome 64 (1993) no. 2, pp. 203-214.

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Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for submanifolds in Riemannian manifolds and in S-manifolds, respectively, which we shall use later. In Section 3, we introduce normal CR-submanifolds of S-manifolds and we study some properties of their geometry. Finally, in Section 4, we consider those submanifolds in the case of the ambient S-manifold being an S-space form.
DOI : 10.4064/cm-64-2-203-214
Keywords: S-manifolds, normal CR-submanifolds, S-space forms

José Cabrerizo 1 ; Luis Fernández 1 ; Manuel Fernández 1

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José Cabrerizo; Luis Fernández; Manuel Fernández. On normal CR-submanifolds of S-manifolds. Colloquium Mathematicum, Tome 64 (1993) no. 2, pp. 203-214. doi : 10.4064/cm-64-2-203-214. http://geodesic.mathdoc.fr/articles/10.4064/cm-64-2-203-214/

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