×

Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. (English) Zbl 1202.53024

Summary: We study the geometry of light-like hypersurfaces of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a light-llke hypersurface. In addition to these main theorems, we study the geometry of totally geodesic light; like hypersurfaces of an indefinite Sasakian manifold.

MSC:

53B25 Local submanifolds
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] C. Atindogbe and K. L. Duggal, Conformal screen on lightlike hypersurfaces, International J. of Pure and Applied Math., 11(4) (2004), 421–442. · Zbl 1057.53051
[2] C. Călin, Contributions to geometry of CR-submanifold, Thesis, University of Iasi (Romania, 1998).
[3] B. Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York, 1973.
[4] K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Acad. Publishers, Dordrecht, 1996. · Zbl 0848.53001
[5] K. L. Duggal and D. H. Jin, Null curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, 2007. · Zbl 1144.53002
[6] K. L. Duggal and D. H. Jin, A classification of Einstein lightlike hypersurfaces of a Lorentzian space form, to appear in J. Geom. Phys. · Zbl 1207.53064
[7] K. L. Duggal and B. Sahin, Lightlike Submanifolds of indefinite Sasakian manifolds, Int. J. Math. and Math. Sci., 2007, Art. ID 57585, 21 pages, Doi:10.1155/2007/57585. · Zbl 1147.53044
[8] K. L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike Submanifolds of indefinite Sasakian manifolds, Acta Math. Hungar., 2008, DOI:10.1007/ s10474-008-7221-8. · Zbl 1265.53039
[9] D. H. Jin, Screen conformal lightlike hypersurfaces of a semi-Riemannian space form, J. Korea Soc. Math. Educ. Ser. B: Pure Appl. Math., 16(3), (2009), 271–276. · Zbl 1180.53020
[10] D. H. Jin, Lightlike hypersurfaces with totally umbilical screen distributions, Chungcheong Math. Soc., 22(3), 2009, 409–416.
[11] D. H. Jin, Screen conformal lightlike real hypersurfaces of an indefinite complex space form, Bull. Korean Math. Soc., 2009, 341–353. · Zbl 1193.53048
[12] D. H. Jin, Lightlike real hypersurfaces with totally umbilical screen distributions, Commun. Korean Math. Soc., 2009, 225–234.
[13] T. H. Kang, S. D. Jung, B. H. Kim, H. K. Pak and J. S. Pak, Lightlike hypersurfaces of indefinite Sasakian manifolds, Indian J. Pure and Appl., Math., 34 (2003), 1369–1380. · Zbl 1046.53053
[14] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983.
[15] T. Takahashi, Sasakian manifolds with pseudo-Riemannian metric, Tôhoku Math. J., 21 (1969), 271–290. · Zbl 0187.43601 · doi:10.2748/tmj/1178242996
[16] S. Tanno, Sasakian manifolds with constant J-holomorphic sectional curvature, Tôhoku Math. J., 21 (1969), 501–507. · Zbl 0188.26801 · doi:10.2748/tmj/1178242960
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.