Keywords:-
Article Content:-
Abstract
In this paper, we study -concircularly flat and pseudo-concircularly flat 3 -dimensional contact metric generalized ( k , ) -space form and such a space form with concircular curvature tensor C satisfying the condition C ( , X ) S = 0 , where S denotes the Ricci curvature tensor. MSC(2010): 53C25, 53D15.
References:-
References
P. Alegre, D. E. Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math., 141 (2004),
-183.
P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Differential Geom. and its
application 26 (2008), 656-666.
P. Alegre and A. Carriazo, Submanifolds of generalized Sasakian-space-forms, Taiwanese J. Math.,
(2009), 923-941.
P. Alegre and A. Carriazo, Generalized Sasakian space forms and conformal change of metric, Results
Math. 59 (2011), 485-493.
D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math., 509, Springer-Verlag,
D. E. Blair, T. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfying a nullity
condition, Israel J. Math., 19 (1995), 189-214.
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, pp. 883-892.
E. Boeckx, A full classification of contact metric ( k , ) -spaces, Illinois J. Math., 44 (2000), 212-219.
A. Carriazo, V .M. Molina and M. M. Tripathi, Generalized ( k , ) -Space Forms, Mediterr.J. Math.,
DOI 10.1007/s00009-012-0196-2.U. C. De and A. Sarkar, Some results on generalized Sasakian-space-forms, Thai J. Math. 8(1) (2010),
-10.
U. C. De and A. Sarkar, On the projective curvature tensor of generalized Sasakian-space-forms,
Quaestiones Mathematicae, 33(2) (2010), 245-252.
U. K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric generalized
Sasakian-space-forms, Note di matemetica 26 (2006), 55-67.
T. Koufogiorgos, Contact Riemannian manifolds with constant -sectional curvature, Tokyo J. Math.,
(1997), 55-67.
D. G. Prakasha, On generalized Sasakian-space-forms with Weyl-conformal curvature tensor,
Lobacheviskii J. Math., 33 (3) (2012), 223-228.
D. G. Prakasha, S. K. Hui and K. K. Mirji, On 3-Dimensional Contact Metric Generalized ( k , )
-Space Forms, Int. J. Math. Math. Sci., Volume 2014, Article ID 797162, 6 pages.
C. R. Premalatha and H. G. Nagaraja, Recurrent generalized ( k , ) –space forms, Acta Universitatis
Apluensis, No. 38/2014, pp. 95-108.
M. M. Tripathi and J. -S. Kim, On the concircular curvature tensor of a ( k , ) -manifold, Balkan J. Geom.
Appl., 9, No. 5, (2004), pp. 104-114.