zbMATH — the first resource for mathematics

Lightlike submanifolds of indefinite Sasakian manifolds. (English) Zbl 1147.53044
The article considers invariant light-like submanifolds of indefinite Sasakian manifolds. In particular, the foliations of submanifolds of codimension two are studied. To understand such submanifolds better, the contact Cauchy-Riemann light-like submanifolds and contact screen Cauchy-Riemann light-like submanifolds are introduced. The article proceeds to examine their properties, including the integrability conditions of their distributions, and the conditions for their existence and minimality.

53C40 Global submanifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
Full Text: DOI EuDML
[1] K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, vol. 364 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. · Zbl 0848.53001
[2] V. I. Arnol’d, “Contact geometry: the geometrical method of Gibbs’s thermodynamics,” in Proceedings of the Gibbs Symposium (New Haven, CT, 1989), pp. 163-179, American Mathematical Society, Providence, RI, USA, 1990. · Zbl 0737.53029
[3] S. Maclane, Geometrical Mechanics II, Lecture Notes, University of Chicago, Chicago, Ill, USA, 1968. · Zbl 0165.00201
[4] V. E. Nazaikinskii, V. E. Shatalov, and B. Y. Sternin, Contact Geometry and Linear Differential Equations, vol. 6 of De Gruyter Expositions in Mathematics, Walter de Gruyter, Berlin, Germany, 1992. · Zbl 0813.58003
[5] C. C\ualin, Contributions to geometry of CR-submanifold, Thesis.
[6] C. C\ualin, “On the existence of degenerate hypersurfaces in Sasakian manifolds,” Arab Journal of Mathematical Sciences, vol. 5, no. 1, pp. 21-27, 1999. · Zbl 0977.53056
[7] T. H. Kang, S. D. Jung, B. H. Kim, H. K. Pak, and J. S. Pak, “Lightlike hypersurfaces of indefinite Sasakian manifolds,” Indian Journal of Pure and Applied Mathematics, vol. 34, no. 9, pp. 1369-1380, 2003. · Zbl 1046.53053
[8] K. Yano and M. Kon, Structures on Manifolds, vol. 3 of Series in Pure Mathematics, World Scientific, Singapore, 1984. · Zbl 0557.53001
[9] D. N. Kupeli, Singular Semi-Riemannian Geometry, vol. 366 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. · Zbl 0871.53001
[10] K. L. Duggal, “Space time manifolds and contact structures,” International Journal of Mathematics and Mathematical Sciences, vol. 13, no. 3, pp. 545-553, 1990. · Zbl 0715.53032 · doi:10.1155/S0161171290000783 · eudml:46548
[11] T. Takahashi, “Sasakian manifold with pseudo-Riemannian metric,” The Tohoku Mathematical Journal, vol. 21, pp. 271-290, 1969. · Zbl 0187.43601 · doi:10.2748/tmj/1178242996
[12] S. Tanno, “Sasakian manifolds with constant \varphi -holomorphic sectional curvature,” The Tohoku Mathematical Journal, vol. 21, pp. 501-507, 1969. · Zbl 0188.26801 · doi:10.2748/tmj/1178242960
[13] K. L. Duggal and D. H. Jin, “Totally umbilical lightlike submanifolds,” Kodai Mathematical Journal, vol. 26, no. 1, pp. 49-68, 2003. · Zbl 1049.53011 · doi:10.2996/kmj/1050496648
[14] A. Bejancu, Geometry of CR-Submanifolds, vol. 23 of Mathematics and Its Applications (East European Series), D. Reidel, Dordrecht, The Netherlands, 1986. · Zbl 0605.53001
[15] K. L. Duggal and B. Sahin, “Screen Cauchy Riemann lightlike submanifolds,” Acta Mathematica Hungarica, vol. 106, no. 1-2, pp. 137-165, 2005. · Zbl 1083.53063 · doi:10.1007/s10474-005-0011-7
[16] C. L. Bejan and K. L. Duggal, “Global lightlike manifolds and harmonicity,” Kodai Mathematical Journal, vol. 28, no. 1, pp. 131-145, 2005. · Zbl 1084.53058 · doi:10.2996/kmj/1111588042
[17] K. L. Duggal and B. Sahin, “Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds,” Acta Mathematica Hungarica, vol. 112, no. 1-2, pp. 107-130, 2006. · Zbl 1121.53022 · doi:10.1007/s10474-006-0068-y
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.