ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES

Yıl 2012, Cilt: 5 Sayı: 2, 95 - 167, 30.10.2012

Mukut Mani Trıpathı , Punam Gupta

Öz

 

Anahtar Kelimeler

T -curvature tensor, quasi-conformal curvature tensor, conformal curvature tensor, conharmonic curvature tensor, pseudo-projective curvature tensor, projective curvature tensor, M-projective curvature tensor

Kaynakça

• [1] J.K. Beem and P.E. Ehrlich, Global Lorentzian geometry, Marcel Dekker, New York, 1981.
• [2] D.E. Blair, Contact manifolds in Riemannian geometry, Lectures Notes in Mathemat- ics, Springer-Verlag, Berlin, 509 (1976), 146.
• [3] D.E. Blair, J.-S. Kim and M.M. Tripathi, On the concircular curvature tensor of a contact metric manifold, J. Korean Math. Soc. 42 (2005), no. 5, 883–892.
• [4] R. Deszcz, On Ricci-pseudosymmetric warped products, Demonstratio Math. 22 (1989), 1053– 1065.
• [5] R. Deszcz, On conformally flat Riemannian manifolds satisfying certain curvature condi- tions, Tensor (N.S.) 49 (1990), 134-145.
• [6] R. Deszcz, Examples of four-dimensional Riemannian manifolds satisfying some pseudosym- metry curvature conditions, Geometry and Topology of Submanifolds, II, Avignon, May, 1988, World Sci. Publ., Singapore 1990, 134-145.
• [7] R. Deszcz, On four-dimensional Riemannian warped product manifolds satisfying certain pseudosymmetry curvature conditions, Colloq. Math. 62 (1991), 103-120.
• [8] R. Deszcz and W. Grycak, On some class of warped product manifolds, Bull. Inst. Math. Acad. Sinica 15 (1987), 311–322.
• [9] R. Deszcz and W. Grycak, On manifolds satisfying some curvature conditions, Colloq. Math. 57 (1989), 89–92.
• [10] R. Deszcz, L. Verstraelen and S. Yaprak, Pseudosymmetric hypersurfaces in 4-dimensional spaces of constant curvature, Bull. Inst. Math. Acad. Sinica 22 (1994), no. 2, 167–179.
• [11] K.L. Duggal, Space time manifolds and contact structures, Internat. J. Math. Math. Sci. 13(1990), 545-554.
• [12] L.P. Eisenhart, Riemannian Geometry, Princeton University Press, 1949. [13] Y. Ishii, On conharmonic transformations, Tensor (N.S.) 7 (1957), 73–80.
• [14] S. Hong, C. Özgür and M.M. Tripathi, On some classes of Kenmotsu manifold, Kuwait J. Sci. Engrg. 33 (2006), no. 2, 19–32.
• [15] K. Kenmotsu, A class of almost contact Riemannian manifold, Tˆohoku Math. J. (2) 24 (1972), 93–103.
• [16] K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Nat. Sci. 12 (1989), no. 2, 151–156.
• [17] B. O’Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, London, 1983.
• [18] C. On a class of para-Sasakian manifold, Turk. J. Math. 29 (2005), 249–257.
• [19] C. Özgür, On Kenmotsu manifolds satisfying certain pseudosymmetry conditions, World Applied Sciences Journal 1 (2006), no. 2, 144–149.
• [20] G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistic significance, Yoko- hama Math. J. 18 (1970), 105–108.
• [21] G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistic significance II, Yokohama Math. J. 19 (1971), no. 2, 97–103.
• [22] G.P. Pokhariyal, Relativistic significance of curvature tensors, Internat. J. Math. Math. Sci. 5 (1982), no. 1, 133–139.
• [23] B. Prasad, A pseudo projective curvature tensor on a Riemannian manifold, Bull. Calcutta Math. Soc. 94 (2002), no. 3, 163–166.
• [24] M. Prvanovi´c, On SP-Sasakian manifold satisfying some curvature conditions, SUT J. Math. 26 (1990), 201–220.
• [25] S. Sasaki, On differentiate manifolds with certain structures which are closely related to almost contact structure I, Tˆohoku Math. J. 12 (1960), 459-476.
• [26] I. Satö, On a structure similar to the almost contact structure, Tensor (N.S.) 30 (1976), no. 3, 219-224.
• [27] T. Takahashi, Sasakian manifold with pseudo-Riemannian metric, Tˆohoku Math J. 21 (1969), 271–290.
• [28] S. Tanno, Ricci curvatures of contact Riemannian manifolds, Tˆohoku Math J. 40 (1988), 441–448.
• [29] M.M. Tripathi, E. Kılıc¸, S. Yu¨ksel Perkta¸s and S. Kele¸s, Indefinite almost paracontact metric manifolds, Internat. J. Math. Math. Sci. 2010 (2010), 19 pp. Art. ID 846195.
• [30] M.M. Tripathi and P. Gupta, T -curvature tensor on a semi-Riemannian manifolds, Jour. Adv. Math. Stud. 4 (2011), no. 1, 117–129.
• [31] M.M. Tripathi and P. Gupta, On (N (k), ξ)-semi-Riemannian manifolds: Semisymmetry, Preprint.
• [32] K. Yano, Concircular Geometry I. Concircular transformations, Math. Institute, Tokyo Im- perial Univ. Proc. 16 (1940), 195–200.
• [33] K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.
• [34] K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom. 2 (1968), 161–184.