Yarı Devirli Ricci Simetrik Manifoldlar Üzerine

Year 2011, Volume: 6 Issue: 1, 73 - 81, 16.05.2011

Shyamal Hui

Abstract

Özet: Bu makalenin amacı, konsirkular simetrik (PCRS)n, konsirkular tekrarlı (PCRS)n, ayrışabilir (PCRS)n manifoldları incelemektir. (PCRS)n ayrışabilir manifoldunda ayrışımlardan birisinin Ricci düzlemsellik (flat), diğerinin de devirli paralellik olduğu gösterilmiştir. Aynı zamanda (PCRS)n nin tümüyle umbilik hiperyüzeyleri çalışılmıştır.

Keywords

Konsirkular simetrik manifold, Konsirkular tekrarlı manifold, Ayrışabilir manifold, Yarı devirli Ricci simetrik manifold, Tümüyle umbilik hiperyüzeyler

On Pseudo Cyclic Ricci Symmetric Manifolds

Abstract

Abstract: The object of the present paper is to study concircularly
symmetric (PCRS)n, concircularly recurrent (PCRS)n, decomposable
(PCRS)n. Among others it is shown that in a decomposable (PCRS)n one of
the decompositions is Ricci flat and the other decomposition is cyclic
parallel. The totally umbilical hypersurfaces of (PCRS)n are also
studied.

Keywords

Concircularly symmetric manifold, Concircularly recurrent manifold, Decomposable manifold, Pseudo cyclic Ricci symmetric manifold, Totally umbilical hypersurfaces

References

• Patterson E.M., 1952. Some theorems on Ricci-recurrent spaces, Journal of London Mathematical Society, 27, 287-295.
• Szabo Z.I., 1982. Structure theorems on Riemannian spaces satisfying R(X,Y). R = 0, The local version, Journal of Differential Geometry, 17, 531-582.
• Chaki M.C., 1988. On pseudo Ricci symmetric manifolds, Bulgarian Journal of Physics, 15, 526-531.
• Shaikh A.A., Hui S.K., 2009. On pseudo cyclic Ricci symmetric manifolds, Asian-European Journal of Mathematics, 2 (2): 227-237.
• Shaikh A.A., Hui S.K., 2010. On pseudo cyclic Ricci symmetric manifolds admitting semi-symmetric connection, Scientia, Series A: Mathematical Sciences, 20, 73-80.
• Shaikh A.A., Hui S.K., 2010. On pseudo cyclic Ricci symmetric spacetimes, Advanced Studies in Contemporary Mathematics, 20 (3): 425-432.
• Shaikh A.A., Hui S.K., 2011. Some global properties of pseudo cyclic Ricci symmetric manifolds, Applied Sciences, 13, 97-101.
• Özen F., Altay S., 2001. On weakly and pseudo symmetric Riemannian spaces, Indian Journal of Pure and Applied Mathematics, 33 (10): 1477-1488.
• Özen F., Altay S., 2008. On weakly and pseudo concircular symmetric structures on a Riemannian manifold, Acta Universitatis Palackianae Olomucensis Facultas Rerum Naturalium, Mathematica, 47, 129-138.
• Shaikh A.A., Roy I., Hui S. K., 2010. On totally umbilical hypersurfaces of weakly conharmonically symmetric spaces, Global Journal Science Frontier Research, 10 (4): 28-30.
• Khan Q., 2004. On recurrent Riemannian manifolds, Kyungpook Mathematical Journal, 44, 269-276.
• Ruse H.S., 1947. Three dimensional spaces of recurrent curvature, Proceedings of London Mathematical Society, 50 (2): 438-446.
• Yano K., Kon M., 1986. Structure on manifolds, Series in Pure Mathematics,Vol. 3, World Scientific Publishing, Singapore.
• Chen B.Y., 1973. Geometry of submanifolds, Marcel-Dekker, New York, p. 298.
• Eisenhart L.P., 1949. Riemannian Geometry, Princeton University Press, Princeton, New Jersey, p. 306.