Generalized Sasakian-Space-Forms admitting Quarter–Symmetric Metric Connection

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-51 Number-5
Year of Publication : 2017
Authors : S.K. Pandey, R. L. Patel, R. N. Singh
  10.14445/22315373/IJMTT-V51P543

MLA

S.K. Pandey, R. L. Patel, R. N. Singh "Generalized Sasakian-Space-Forms admitting Quarter–Symmetric Metric Connection", International Journal of Mathematics Trends and Technology (IJMTT). V51(5):321-331 November 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
The object of the present paper is to study generalized Sasakian-space-forms admitting quarter-symmetric metric connection. The relation between the curvature tensors of quarter-symmetric metric connection and linear connection has been obtained. Also, the properties of projective and conformal curvature tensors of quarter-symmetric metric connection on a generalized Sasakian-space–form have been studied.

Reference
[1] Alegre, P., Blair, D. E. and Carriazo, A. (2004): Generalized Sasakian-space-forms, Israel Journal ofMathematics, vol. 141, pp. 157–183, 2004.
[2] Alegree, P. and Carriazo, A. (2008): Structures on generalized Sasakian-space-forms, Differential Geometry and its Applications, Vol.26, no6, pp. 656-666.
[3] Alegree, P. andCarriazo, A. (2011): Generalized Sasakian–space–forms and conformal changes of the metric, Results in Mathematics, Vol.59, no.3-4,pp. 485-493.
[4] Alegre, P., Carriazo,A., Kim, Y. H. and Yoon, D.W.(2007):B.Y. Chen‟s inequality forsubmanifolds of generalized space forms,Indian Journal of Pure and Applied Mathematics,vol.38, no.3,pp.185-201.
[5] Al-Ghefari, R., Al-Solamy, F. R. and Shahid,M.H. (2006): CR-submanifolds of generalized space forms,JP Journal of Geometry and Topology, vol.6,no.2,pp.151-166.
[6] Al-Ghefari, R., Al-Solamy, F. R. and Shahid,M.H. (2006): Contact CR-warped productsubmanifolds in generalized Sasakian space forms,Balkan Journal of Geometry and its Applications, vol.11,no.2,pp.1-10.
[7] Biswas, S. C. and De, U. C. (1997): Quarter-symmetric metric connection in an SP-Sasakian manifold, Commun. Fac. Sci. Univ. Ank. Series, 46,49-56.
[8] Blair, D. E. (2002): Riemannian geometry of contact and symplectic manifolds, progress in Mathrmatics,203, Birkhauser Boston, Inc., M.A.
[9] De, U. C. and De, K. (2011): On three dimensional Kenmotsu manifolds admitting a quarter-symmetric metric connection, Azerbaijan Journal of Mathematics,1(2),132-142.
[10] De, U. C. andMondal, A. K. (2008): Quarter-symmetric metric connection on a Sasakian manifold, Bull. Math. Analysis and Application, 1,99-108.
[11] De, U. C. and Sarkar, A. (2010): “On the projective curvature tensor of generalized Sasakian-space-forms,” QuaestionesMathematicae,vol.33,no.2,pp.245-252.
[12] De, U. C., Singh, R. N. and Pandey, Shravan K. (2012): On Conharmonic Curvature Tensor of Generalized Sasakian-Space-forms volume 2012, Article ID 876276, 14.
[13] Friedmann, A. and Schouten, J. A (1924): Uber die geometric der halbsymmetrischenubertragun, Math. Zeitschr. 21,211-233.
[14] Golab, S. (1975): On semi-symmetric and quarter-symmetric linear connections, Tensor (N.S.),29, 249-254.
[15] Kim, U. K. (2006): Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian–space-forms, “Note di Mathematica,Vol.no.1,pp.55-67.
[16] Singh, R. N.,Pandey, S. K. (2013): On generalized Sasakian-space-forms, The Mathematics Student, 81(1-4), 205-213.
[17] Singh, R. N.,Pandey, S. K. and Tiwari, Kiran (2013):On quarter-symmetric Metric connection in indefinite Sasakian Manifold, Journal of International Academy of Physical Sciences,17 (3),255-275.
[18] Singh, R.N. and Pandey,Shravan K.(2013):On the C-Bochner Curvature tensor of generalized Sasakian Space-forms,J. Tensor Society,7,17-28, 2013.
[19] Singh, R. N. and Pandey, S. K.,(2014) On a quarter-symmetric metric connection in an LP-Sasakian manifold, Thai J. Math., 12 (2), 357-371.
[20] Xufeng, X. and Xiaoli,C. (1998): Two theorems on

keywords
generalized Sasakian-space-form, quarter-symmetric metric connection, projective curvature tensor and conformal curvature tensor,