ON THE W5-CURVATURE TENSOR OF GENERALIZED SASAKIAN-SPACE-FORMS

Year 2016, Volume: 4 Issue: 1, 45 - 53, 01.04.2016

D. G. Prakasha , Vasant Chavan Kakasab Mırjı

Abstract

The object of the paper is to characterize generalized Sasakian- space-forms satisfying certain curvature conditions on W5-curvature tensor. We characterizeW5- at, -W5- at and -W5-semisymmetric generalized Sasakian- space-forms.

Keywords

Generalized Sasakian-space-forms; W5-curvature tensor; W5- at; - W5- at; -W5-semisymmetric.

References

• [1] P. Alegre, D. E Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math., 14 (2004), 157{183.
• [2] P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Di. Geo. and its Application, 26 (2008), 656{666.
• [3] P. Alegre and A. Carriazo, Submanifolds generalized Sasakian-space-forms, Taiwanese J. Math., 13 (2009), 923{941.
• [4] P. Alegre and A. Carriazo, Generalized Sasakian-space-forms and conformal change of met- ric, Results Math., 59 (2011), 485{493.
• [5] D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509, Springer-Verlag, 1976.
• [6] U. C. De and A. Sarkar, On the projective curvature tensor of generalized Sasakian-space- forms, Quaestiones Mathematicae, 33 (2010), 245{252.
• [7] U. C. De, R. N. Singh and S. K. Pandey, On the conharmonic curvature tensor of generalized Sasakian-space-forms, ISRN Geometry, (2012), Article ID 876276, 14 pages doi:10.5402/2012/876276
• [8] U. C. De and P. Majhi, -semisymmetric generalized Sasakian-space-forms, Arab J Math Sci., 21 (2015), 170{178.
• [9] S. K. Hui and D. G. Prakasha, On the C-Bochner curvature tensor of generalized Sasakian- space-forms, Proc. Natl. Acad. Sci., India. Sect. A Phys. Sci. 85(3) (2015), 401-405.
• [10] S. K. Hui and A. Sarkar, On the W2-curvature tensor of generalized Sasakian-space-forms, Math. Pannonica, 23(1) (2012), 113{124.
• [11] U. K. Kim, Conformally at generalized Sasakian-space-forms and locally symmetric gener- alized Sasakian-space-forms, Note di Matematica, 26 (2006), 55{67.
• [12] G. P. Pokhariyal, Relativistic signicance of curvature tensors, Internat. J. Math & Math. Sci.,5(1) (1982), 133-139.
• [13] D. G. Prakasha, On generalized Sasakian-space-forms with Weyl-conformal curvature tensor, Lobachevskii J. Math., 33(3)(2012), 223{228.
• [14] D. G. Prakasha and H. G. Nagaraja, On quasi-conformally at and quasi-conformally semisymmetric generalized Sasakian-space-forms, Cubo (Temuco) 15(3) (2013), 59{70.
• [15] D. G. Prakasha and V. Chavan On weak symmetries of generalized Sasakian-space-forms, Communications in Mathematics and Applications, 5 (3) (2014), 83{89.
• [16] A. Sarkar and A. Akbar, Generalized Sasakian-space-forms with projective curvature tensor, Demonstr. Math., XLVII(3) (2014), 726{738.
• [17] A. Sarkar, M. Sen and A. Akbar, Generalized Sasakian-space-forms with conharmonic cur- vature tensor, Palestine J. Math., 4 (1) (2015), 84{90.