On T-Curvature Tensor In K-Contact And Sasakian Manifolds

Year 2011, Volume: 4 Issue: 1, 32 - 47, 30.04.2011

Mukut Mani Tripathi Punam Gupta

Abstract

Keywords

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

References

• [1] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Progress in Mathe- matics, 203 (Boston, MA: Birkhauser Boston, Inc.) (2002).
• [2] Boothby, W. M. and Wang, H. C., On contact manifolds, Ann. Math., 68 (1958), 721–734.
• [3] Cabrerizo, J. L., Ferna´ndez, L. M., Ferna´ndez, M. and Zhen, G., The structure of a class of K-contact manifolds, Acta Math. Hungar., 82 (1999), no. 4, 331–340.
• [4] Dwivedi, M. K. and Kim, J.-S., On conharmonic curvature tensor in K-contact and Sasakian manifolds, Bull. Malays. Math. Sci. Soc. 34(1) (2011), 171-180.
• [5] Eisenhart, L. P., Riemannian Geometry, Princeton University Press, 1949. [6] Ishii, Y., On conharmonic transformations, Tensor (N.S.), 7 (1957), 73–80.
• [7] Ogiue, K., On fibrings of almost contact manifolds, Kodai Math. Sem. Rep., 17 (1965) 53–62.
• [8] Pokhariyal G. P. and Mishra, R. S., Curvature tensors and their relativistic significance, Yokohama Math. J., 18 (1970), 105–108.
• [9] Pokhariyal, G. P. and Mishra, R. S., Curvature tensors and their relativistic significance II, Yokohama Math. J., 19 (1971), no. 2, 97–103.
• [10] Pokhariyal, G. P., Relativistic significance of curvature tensors, Internat. J. Math. Math. Sci., 5 (1982), no. 1, 133–139.
• [11] Prasad, B., A pseudo projective curvature tensor on a Riemannian manifold, Bull. Calcutta Math. Soc., 94 (2002), no. 3, 163–166.
• [12] Tripathi, M. M. and Dwivedi, M. K., The structure of some classes of K-contact manifolds, Proc. Indian Acad. Sci. (Math. Sci.), 118 (2008), no. 3, 371–379.
• [13] Tripathi, M. M. and Gupta, P., T -curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Stud. 4 (2011), No. 1, 117-129.
• [14] Yano, K., Concircular Geometry I. Concircular transformations, Math. Institute, Tokyo Im- perial Univ. Proc., 16 (1940), 195–200.
• [15] Yano, K. and Bochner, S., Curvature and Betti numbers, Annals of Mathematics Studies 32, Princeton University Press, 1953.
• [16] Yano, K. and Sawaki, S., Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2 (1968), 161–184.
• [17] Zhen, G., Cabrerizo, J. L., Ferna´ndez, L. M. and Fern´andez, M., On ξ-conformally flat contact metric manifolds, Indian J. Pure Appl. Math., 28 (1997), 725–734.
• [18] Zhen, G., On conformal symmetric K-contact manifolds, Chinese Quart. J. Math., 7 (1992), 5–10.