Symmetries of Sasakian Generalized Sasakian-Space-Form Admitting Generalized Tanaka–Webster Connection

Main Article Content

Chawngthu Lalmalsawma
https://orcid.org/0000-0001-7929-482X
Jay Prakash Singh

Abstract

The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.

Article Details

How to Cite
Lalmalsawma, C., & Singh, J. P. (2021). Symmetries of Sasakian Generalized Sasakian-Space-Form Admitting Generalized Tanaka–Webster Connection. Tamkang Journal of Mathematics, 52(2), 229–240. https://doi.org/10.5556/j.tkjm.52.2021.3246
Section
Papers
Author Biography

Jay Prakash Singh, Mizoram University

Assistant Professor

Mathematics and computer science departmant

References

A. Akbar and A. Sarkar. Some results on a generalized Sasakian space forms admitting trans Sasakian structure with respect to generalized Tanaka Webster okumara connection, Romanian

Journal of Mathematics and Computer Science 5(2) (2015), 130-137.

P. Alegre, D.E. Blair and A. Carriazo, Generalized Sasakian-space-forms, Israel journal of mathematics 141(1) (2004), 157-183.

P. Alegre and A. Carriazo, Semi-Riemannian Generalized Sasakian Space Forms, Bulletin of the Malaysian Mathematical Sciences Society (2018), 1-14.

P. Alegre and A. Carriazo, Structures on generalized Sasakian-space-forms, Dierential Geometry and its Applications 26(6) (2008), 656-666.

D.E. Blair, Contact manifolds in Riemannian geometry, Springer-Verlag Berlin, Heidelberg, (1976).

M.C. Chaki, On pseudosymmetric manifolds, An. Stiint. Univ. AL.I. Cuza din Iasi Sect. I-a Math. N.S. 33(1) (1987), 5358.

U.C. De and G. Ghosh, On generalized TanakaWebster connection in sasakian manifold, Bulletin of the Transilvania University of Brasov. Mathematics, Informatics, Physics. Series III 9(2) (2016), 13pp.

U.C. De and P. Majhi, Certain curvature properties of generalized Sasakian-space-forms, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 83(2) (2013), 137-141.

U.C. De and P. Majhi, On the Q curvature tensor of a generalized Sasakian-space-form, Kragujevac Journal of Mathematics 43(3) (2019), 333-349.

U.C. De, and A. Sarkar, On the conharmonic turvature tensor of generalized Sasakian-space-forms, ISRN Geometry, https://doi:10.5402/2012/876276,(2012).

U.C. De, and A. Sarkar, On the projective turvature tensor of generalized Sasakian-space-forms, Quaestiones Mathematicae 33(2) (2010), 245-252.

U. C. De and P. Majhi, : -semisymmetric generalized Sasakian space-forms, Kragujevac Journal of Mathematics 21(1) (2015), 170-178.

R. Deszcz, On pseudosymmetric spaces, Bull. Belg. Math. Soc., Ser. A 44 (1992), 134.

A. Friedmann and J.C. Schouten, Uber die Geometric der halbsymmetrischen Ubertragung, Math. Zeitschr. 21 (1924), 211223.

S. Kishor, P. Verma and P. K. Gupt, On W9-Curvature Tensor of Generalized Sasakian-Space-Forms, Int. J. of Math. Appl 5 (2017), 103-112.

J. de Dios Prez and Y. J. Suh, Generalized TanakaWebster and covariant derivatives on a real hypersurface in a complex projective space, Monatshefte fr Mathematik 177(4) (2015), 637-647.

A. Sarkar and U. C. De, Some curvature properties of generalized Sasakian-space-forms, Lobachevskii Journal of Mathematics 33(1) (2012), 22-27.

J. P. Singh, Generalized Sasakian space forms with m-projective curvature tensor, Acta Math. Univ. Comenianae 85(1) (2016), 135-146.

J. P. Singh, On a type of generalized Sasakian space forms, Journal of the Indian Math. Soc. 83(3-4) (2016), 363-372.

S. Sular and C. zgur, Generalized Sasakian space forms with semi-symmetric metric connections, Annals of the Alexandru Ioan Cuza University-Mathematics, 60(1) (2014), 145-156.

S. Sular and C. zgur, Generalized Sasakian space forms with semi-symmetric non-metric connections, Proceedings of the Estonian Academy of Sciences, 60(4)(2011), 251-257.

N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japanese journal of mathematics. New series, 2(1) (1976), 131-190.

S. Tanno, Variational problems on contact Riemannian manifolds, Transactions of the American Mathematical society 314(1) (1989), 349-379.

S. M. Webster, Pseudohermitian structures on a real hypersurface, J. Differ. Geom. 13 (1978), 2541.

K. Yano and M. Kon, Structures on manifolds, World scientic, (1985).

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

Z. I. Szabo, Structure theorems on Riemannian spaces satisfying R(X; Y ):R = 0. II. Global versions, Geometriae Dedicata 19(1) (1985), 65-108.