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

Year 2012, Volume: 5 Issue: 2, 95 - 167, 30.10.2012

Mukut Mani Trıpathı , Punam Gupta

Abstract



 

Keywords

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

References

  • [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.

Year 2012, Volume: 5 Issue: 2, 95 - 167, 30.10.2012

Mukut Mani Trıpathı , Punam Gupta

Abstract

References

  • [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.
There are 33 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mukut Mani Trıpathı

Punam Gupta This is me

Publication Date October 30, 2012
Published in Issue Year 2012 Volume: 5 Issue: 2

Cite

APA Trıpathı, M. M., & Gupta, P. (2012). ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES. International Electronic Journal of Geometry, 5(2), 95-167.
AMA Trıpathı MM, Gupta P. ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES. Int. Electron. J. Geom. October 2012;5(2):95-167.
Chicago Trıpathı, Mukut Mani, and Punam Gupta. “ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES”. International Electronic Journal of Geometry 5, no. 2 (October 2012): 95-167.
EndNote Trıpathı MM, Gupta P (October 1, 2012) ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES. International Electronic Journal of Geometry 5 2 95–167.
IEEE M. M. Trıpathı and P. Gupta, “ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES”, Int. Electron. J. Geom., vol. 5, no. 2, pp. 95–167, 2012.
ISNAD Trıpathı, Mukut Mani - Gupta, Punam. “ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES”. International Electronic Journal of Geometry 5/2 (October 2012), 95-167.
JAMA Trıpathı MM, Gupta P. ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES. Int. Electron. J. Geom. 2012;5:95–167.
MLA Trıpathı, Mukut Mani and Punam Gupta. “ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES”. International Electronic Journal of Geometry, vol. 5, no. 2, 2012, pp. 95-167.
Vancouver Trıpathı MM, Gupta P. ON (N(k);ξ)-SEMI-RIEMANNIAN MANIFOLDS: PSEUDOSYMMETRIES. Int. Electron. J. Geom. 2012;5(2):95-167.