ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLD
| Autor: | S. K. Pandey, R. N. Singh, Giteshwari Pandey, Kiran Tiwari |
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| Rok vydání: | 2014 |
| Předmět: |
Christoffel symbols
Riemann curvature tensor Pure mathematics Applied Mathematics General Mathematics Mathematical analysis Holonomy Fundamental theorem of Riemannian geometry Levi-Civita connection Pseudo-Riemannian manifold symbols.namesake symbols Mathematics::Differential Geometry Ricci curvature Metric connection Mathematics |
| Zdroj: | Communications of the Korean Mathematical Society. 29:331-343 |
| ISSN: | 1225-1763 |
| Popis: | The object of the present paper is to study a semi-symmetricmetric connection in an (e)-Kenmotsu manifold. In this paper, we studya semi-symmetric metric connection in an (e)-Kenmotsu manifold whoseprojective curvature tensor satisfies certain curvature conditions. 1. IntroductionThe idea of a semi-symmetric linear connection on a differentiable manifoldwasfirstintroducedby Friedmannand Schouten[11] in 1924. Hayden[12] intro-duced a semi-symmetric metric connection on a Riemannian manifold. Yano[21] proved the theorem: A Riemannian manifold admits a semi-symmetricmetric connection whose curvature tensor vanishes if and only if Riemannianmanifold is conformally flat. Semi-symmetric metric connections on a Rie-mannian manifold have been studied by Amur and Pujar [1], Pravanovic [15],Binh [4], De ([6], [7]), De and Biswas [8], Sharfuddin and Hussain [16], Pathakand De [14], Jun, De and Pathak [13], Barman and De [2], Chaubey and Ojha[5], Singh and Pandey [17], Singh, Pandey and Pandey ([18], [19]) and manyothers.Duggal and Sharma [10] studied a semi-symmetric metric connection in asemi-Riemannian manifold. They studied some properties of the Ricci tensor,affine conformal motions, geodesics and group manifolds with respect to thesemi-symmetric metric connection. On the other hand, the study of manifoldswith indefinite metrics is of interest from the standpoint of physics and relativ-ity. Manifolds with indefinite metrics have been studied by several authors. In1993, Bejancu and Duggal [3] introduced the concept of (e)-Sasakian manifoldsand Xufeng and Xiaoli [20] established that these manifolds are real hypersur-faces of indefinite Kahlerian manifolds. Recently De and Sarkar [9] introduced |
| Databáze: | OpenAIRE |
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