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Information Journal Paper

Title

UMBILICITY OF (SPACE-LIKE) SUBMANIFOLDS OF PSEUDO-RIEMANNIAN SPACE FORMS

Pages

  153-157

Keywords

(V−)UMBILICITYQ3

Abstract

 We study (v-) umbilic (space-like) submanifolds of pseudo-Riemannian SPACE FORMs, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone. A pseudo-Riemannian submanifold M in M- (a pseudo Riemannian manifold) is called v -umbilic if the shape operator of M along V Î^c^ (M ) is S=lidTM for some lÎC¥(M) . A totally semi-umbilical space-like submanifold of a pseudo Euclidean space is an space-like sub manifold for which the curvature ellipse degenerates into a segment at every point except perhaps at isolated points. One of our main results says that if Mn is an space-like (immersed) sub manifold of RPn+m  n³2 , then M is totally semi-umbilical and , C ∏x , BÕx (some special normal vectors) are in the same direction for every x ÕÎT xM and all (except isolated) points of M, if and only if there exist linearly independent normal fields Vn+1,…..,Vn+m-1 locally defined at every non-umbilical point of M, such that M is Va-umbilical, n+1£a £n+m-1.

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    APA: Copy

    KASHANI, S.M.B.. (2009). UMBILICITY OF (SPACE-LIKE) SUBMANIFOLDS OF PSEUDO-RIEMANNIAN SPACE FORMS. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 20(2), 153-157. SID. https://sid.ir/paper/84103/en

    Vancouver: Copy

    KASHANI S.M.B.. UMBILICITY OF (SPACE-LIKE) SUBMANIFOLDS OF PSEUDO-RIEMANNIAN SPACE FORMS. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2009;20(2):153-157. Available from: https://sid.ir/paper/84103/en

    IEEE: Copy

    S.M.B. KASHANI, “UMBILICITY OF (SPACE-LIKE) SUBMANIFOLDS OF PSEUDO-RIEMANNIAN SPACE FORMS,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 20, no. 2, pp. 153–157, 2009, [Online]. Available: https://sid.ir/paper/84103/en

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