Totally umbilical radical transversal lightlike hypersurfaces of Kähler-Norden manifolds of constant totally real sectional curvatures

Document Type : Research Paper

Author

Department of Algebra and Geometry‎, ‎Faculty of Mathematics and Informatics‎, ‎University of Veliko Tarnovo‎ ‎"St.‎ ‎Cyril and St‎. ‎Methodius"‎, ‎2 T. Tarnovski Str.‎, ‎5003 Veliko Tarnovo‎, ‎Bulgaria.

Abstract

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,\widetilde g)$ of a K\"ahler-Norden manifold $(\overline M,\overline J,\overline g,\overline { \widetilde g})$ of constant totally real sectional curvatures $\overline \nu$ and $\overline {\widetilde \nu}$ ($g$ and $\widetilde g$ are the induced metrics on $M$ by the Norden metrics $\overline g$ and $\overline {\widetilde g}$, respectively). We obtain a condition for $\overline {\widetilde \nu}$ (resp. $\overline \nu$) which is equivalent to each
of the following conditions: $(M,g)$ $(resp.\, (M,\widetilde g))$ is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We construct an example of a totally umbilical radical transversal lightlike hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein.

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References

A. Borisov and G. Ganchev, Curvature properties of Kaehlerian manifolds with B-metric, 220{226, Proc. of 14th Spring Conference of UBM, Sunny Beach, 1985.
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publishers Group, Dordrecht, 1996.
K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Birkhäuser Verlag, Basel, 2010.
G. T. Ganchev and A. Borisov, Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulgare Sci. 39 (1986), no. 5, 31{34.
G. T. Ganchev, K. Gribachev and V. Mihova, B-connections and their conformal invariants on conformally Kahler manifolds with B-metric, Publ. Inst. Math. (Beograd) (N.S.) 42 (1987), no. 56, 107{121.
D. H. Jin, The curvatures of lightlike hypersurfaces of an indefinite Kenmotsu manifold, BJGA 17 (2012), no. 1, 49{57.
G. Nakova, Some lightlike submanifolds of almost complex manifolds with Norden metric, J. Geom. 103 (2012), no. 2, 293{312.
G. Nakova, Radical transversal lightlike hypersurfaces of almost complex manifolds with Norden metric, J. Geom. 104 (2013), no. 3, 539{556.
A. Norden, On a class of four-dimensional A-spaces (in Russian), Izv. Vyss. Ucebn. Zaved. Matematika 17 (1960) 145{157.
B. Sahin, Lightlike hypersurfaces of semi-Euclidean spaces satisfying curvature conditions of semisymmetry type, Turkish J. Math. 31 (2007), no. 2, 139{162.
Bulletin of the Iranian Mathematical Society
Volume 42, Issue 4 - Serial Number 4
August 2016
Pages 839-854

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History

  • Receive Date: 20 January 2015
  • Revise Date: 07 May 2015
  • Accept Date: 07 May 2015

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