Co-screen conformal half-lightlike submanifolds

Authors

  • Yaning Wang
  • Ximin Liu

DOI:

https://doi.org/10.5556/j.tkjm.44.2013.1232

Keywords:

Half-lightlike submanifold, semi-Riemannian manifold, co-screen conformal, induced Ricci tensor.

Abstract

In this paper, we introduce and study the geometry of half lightlike submanifold $M$ of a semi-Riemannian manifold $\overline{M}$ satisfying that the shape operator of screen transversal bundle is conformal to the shape operator of lightlike transversal bundle of $M$. Using this geometric condition we obtain some results to characterize the unique existence of screen distribution of $M$, also, we present some sufficient conditions for the induced Ricci curvature tensor of $M$ to be symmetric.

Author Biographies

Yaning Wang

Department ofMathematics, South China University of Technology, Guangzhou 510641, Guangdong, P. R. China.

Ximin Liu

School ofMathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, P. R. China.

References

C. Atindogbe, K.L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math. 11(4)(2004), 421-442.

K. L. Duggal, On canonical screen for lightlike submanifolds of codimensional two, Cent. Eur. J. Math. 5(4) (2007), 710-719.

K. L. Duggal, A. Bejancu, Lightlike submainfolds of semi-Riemannian mainfolds and applications, Kluer Academic Publishers, Dordrecht, 1996.

K. L. Duggal, A. Bejancu, Lightlike submanifolds of codimensional two, Math. J. Toyama Univ. 15 (1992), 59-82.

K. L. Duggal, D.H. Jin, Half lightlike submanifolds of codimensional $2$, Math. J. Toyama Univ. 22 (1999), 121-161.

K. L. Duggal, B. Sahin, Screen conformal half-lightlike submainfolds, Int. J. Math. Math. Sci. 68 (2004), 3737-3753.

K. L. Duggal, B. Sahin, Differential geometry of lightlike submanifolds, Birkhauser Veralag AG, Basel, Boston, Berlin, 2010.

D. H. Jin, Einstein half lightlike submanifold with a Killing co-screen distribution, Honam Math. J., 30(3)(2008), 487-504.

D. H. Jin, Special half lightlike submanifolds of an indefinite cosymplectic manifolds, J. Function Spaces Appl. Volume 2012, Article ID 632624, 16 pages.

D. H. Jin, Special half lightlike submanifolds of an indefinite Sasakian manifolds, to appear.

D. N. Kupeli, Singular semi-Riemnnian Geometry, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1996.

B. O'Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, London, 1983.

Downloads

Published

2013-12-31

How to Cite

Wang, Y., & Liu, X. (2013). Co-screen conformal half-lightlike submanifolds. Tamkang Journal of Mathematics, 44(4), 431–444. https://doi.org/10.5556/j.tkjm.44.2013.1232

Issue

Section

Papers