E-BOCHNER CURVATURE TENSOR ON ALMOST C(λ) MANIFOLDS

Brijesh Kumar Gupta, Braj Bhushan Chaturvedi

DOI Number
https://doi.org/10.22190/FUMI220416051G
First page
739
Last page
750

Abstract


The present paper deals the study of E-Bochner curvature tensor on an almost C(λ) manifolds with the conditions Be (ξ, X).S = 0, Be (ξ, X).R = 0, R.Be (ξ, X) = 0 and Be (ξ, X).Be = 0, where R, S and Be denotes Riemannian curvature tensor, Ricci tensor and E-Bochner curvature tensor, respectively. Also, we have studied ξ-E-Bochner flat C(λ) manifolds.

Keywords

Almost contact manifold, E-Bochner curvature tensor, $C({\lambda})$ manifolds, Ricci tensor, Einstien manifold and Pseudosymmetric manifold.

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References


Ali Akbar and Avijit Sarkar, On the conharmonic and concircular curvature tensors of almost C(λ) manifolds, Int. J. of Avanced Mathemathical sciences, 1(3) 2013, 134-138.

A. G. Walker, On Ruses spaces of recurrent curvature, Proc. London Math. Soc. 52(1950), 36-64.

D.E. Blair Contact manifold in Riemannian Geometry, Lecture Notes in Mathematics. Spriger, Berlin, 1976, 509.

D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. j. 4(1981), 1-27.

D. E. Blair, On the geometric meaning of the Bochner tensor, Geom. Dedicata 4(1975), 33-38.

G. Zhen, J. L. Cabrerizo, L. M. Fernandez, and M. Fernandez, On ξ-conformally flat contact metric manifolds, Indian J. Pure Appl. Math.28, (1997), 725-734.

G. Pathak, U. C. De, and Y. H. Kim, Contact manifolds with C-Bochner curvature tensor, Bull. Calcutta Math. Soc.96, (2004), 45-50.

H. Endo, On K-Contact Riemannian manifolds with vanishing E-contact Bochner curvature tensor, Collq. Math. 62 (1991), 293-297.

J. S. Kim, M. M. Tripathi and J.Choi, On C-Bochner curvature tensor of a contact metric manifold, Bull. Korean Math. Soc. 42 (2005), 713-724.

M. Matsumoto and G. Chuman, On the C-Bochner Curvature tensor, TRU Math 5, 21(1969), 21-30.

R. Deszcz, On pseudosymmetric space, Bull. Soc. Math. Belg. Se0r. A, 44(1), 1992,1-34.

S.K. Hui and D.G.Prakasha, On the C-Bochner Curvature tensor of generalised Sasakian-space-forms, Proc. Natl. Acad. Sci.,India, Sect. A Phys. Sci., 85(3), (2015),401-405.

S. V. Kharitonova, Almost C(λ) manifolds, Journal of Mathematical Science,177(2011), 742-747.

S. Bochner, Curvature and Betti numbers, Ann. of Math. 49 (1948), 379-390.

T. Adati and T. Miyazawa, On a Riemannian space with recurrent conformal curvature, Tensor N. S. 18(1967), 348-354.

U.C.De , Ahmet Yildiz, Mine Turan and Bilal E. Acet ,3-Dimensional quasi Sasakian manifolds with semi-symmetric non-metric connection, Hacettepe Journal of Mathematics and Statistics 41 (1) (2012), 127-137.

U.C. De and A.A. Shaikh, Sasakian manifolds with C-Bochner curvature tensor, Indian J. of Math. 41, (1999), 131-137.

W. M. Boothby and H. C. Wang, On contact manifolds, Ann. of Math. 68 (1958),721-734.

Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X,Y).R=0, the local version, J. Diff. Geom. 17(1982), 531-582.




DOI: https://doi.org/10.22190/FUMI220416051G

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