On some classes of invariant submanifolds of lorentzian para-sasakian manifolds

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Srimayee Samui
Uday Chand De

Abstract

The object of the present paper is to study invariant submanifolds of Lorenzian Para-Sasakian manifolds. We consider the recurrent and bi-recurrent invariant submanifolds of Lorentzian para-Sasakian manifolds and pseudo-parallel and generalized Ricci pseudo-parallel invariant submanifolds of Lorentzian para-Sasakian manifolds. Also we search for the conditions $\mathcal{Z}(X,Y)\cdot\alpha=fQ(g,\alpha)$ and $\mathcal{Z}(X,Y)\cdot\alpha=fQ(S,\alpha)$ on invariant submanifolds of Lorentzian para-Sasakian manifolds, where $\mathcal{Z}$ is the concircular curvature tensor. Finally, we construct an example of an invariant submanifold of Lorentzian para Sasakian manifold.

Article Details

How to Cite
Samui, S., & De, U. C. (2016). On some classes of invariant submanifolds of lorentzian para-sasakian manifolds. Tamkang Journal of Mathematics, 47(2), 207–220. https://doi.org/10.5556/j.tkjm.47.2016.1868
Section
Papers
Author Biographies

Srimayee Samui

Umeschandra college, 13, Surya Sen Street, Kol 700012, West Bengal, India.

Uday Chand De

Department of PureMathematics, Calcutta University, 35 Ballygunge Circular Road, Kol 700019, West Bengal, India.

References

A. A. Shaikh and U. C. De, On 3-dimensional Lorentzian para-Sasakian manifolds, Soochow J. Math., 26(2000), 359--368.

A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel immersions of a space forms, Mat. Contemp.,17 (1999), 59--70.

A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-parallel submanifolds of a space forms, Adv. Geom. 2 (2002), 57--71.

B. Y. Chen, Geometry of submanifolds, Pure and Appl. Math. $22$, Marcel Dekker, Inc., New York, 1973.

C. Murathan, K. Arslan and K. Ezentas, Ricci generalized pseudo-symmetric immersions, Diff. Geom. and Appl. Matfypress Prague, (2005), 99--108.

C. Ozgur, On $varphi$-conformally flat Lorentzian para-Sasakian manifolds, Radovi Mathematiki, 12(2003), 99--106.

C. Ozgur and C. Murathan, On invariant submanifolds of Lorentzian para-Sasakian manifolds, The Arab. J. for Sci. and Eng., 34 (2008),177--185.

D. E. Blair, Contact Manifold in Riemannain Geometry, Lecture Notes on Mathematics, 509, Springer-Verlag, Berlin, 1976.

E. Boeckx, O. Kowalski and L. Vanhecke, Riemannian Manifolds of Conullity Two, Singapore World Sci. Publishing, 1996.

F. Dillen, Semiparallel hypersurfaces of a real space form, Israel J. Math., 75 (1991), 193--202.

J. Deprez, Semiparallel surfaces in Euclidean space, J. Geom., 25(1985), 192--200.

J. Deprez, Semiparallel hypersurfaces, Rend. Sem. Mat. Univ. Politechn. Torino, 45(1986), 303--316.

H. Endo, Invariant submanifolds in contact metric manifolds, Tensor (N.S), 43(1986), 83--87.

K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci., 12(1989), 151--156.

K. Matsumoto and I. Mihai, On a certain transformation in a Lorentzian Para-Sasakian manifold, Tensor (N.S), 47(1988), 189--197.

K. Matsumoto, I. Mihai and R. Rosca, $xi$-null geodesic gradient vector fields on a Lorentzian para-Sasakian manifolds, J. Korean Math. Soc., 32 (1995), 17--31.

K. Yano and M. Kon, Structures of manifolds, Series in Pure Math, $3$. World Scientific Publ. Co., Singapore, 1984.

K. Yano, Concircular geometry. I. concircular transformations, Proc. Imp. Acad. Tokyo, 16(1940), 195--200.

L. Verstraelen, Comments on pseudosymmetric in the sence of R. Deszcz, In: Geometry and Topology of submanifolds, VI. River Edge, NJ: World

Sci. Publishing, 1994, 199--209.

M. Kon, Invariant submanifolds of Normal contact metric manifolds, Kodai Math. Sem. Rep., 35(1973), 330--336.

M. M. Tripathi and U. C. De, Lorentzian almost paracontact manifolds and their submanifolds, J. Korea Soc. Math. Educ. SerB: Pure and Appl. Math.,8(2001), 101--125.

P. Majhi, On Some Invariant Submanifolds of Kenmotsu Mnifolds, The Mathematics Student, 82(2013), 1--15.

R. Aikawa and Y. Matsuyama, On local symmetry of Kaehler hypersurfaces, Yokohoma Mathematical J., 51(2005).

U. C. De, A. Al-Aqeel and A. A. Shaikh, Submanifolds of a Lorentzian para-Sasakian manifolds, Bull. Malays. Math. Sci. Soc., 2(28) (2005), 223--227.

U. C. De and A. A. Shaikh, Non-existence of proper semi-invariant submanifolds of Lorentzian para-Sasakian manifold, Bull. Malaysian Math. Sci. Soc., (2),22(2)(1999), 179--183.

V. Mangione, Totally geodesic submanifolds of a Kenmotsu space form, Math. Reports, 7 (57), 4(2005), 315--324.