Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold
-
Abhitosh Upadhyay
and
Ahmad Sharfuddin
Abstract
The paper is mainly devoted to the study of the geometry of screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold. The main result is a characterisation theorem for screen conformal lightlike hypersurfaces of an indefinite cosymplectic space form. The examples of totally geodesic, screen homothetic and screen conformal lightlike hypersurfaces are also given.
References
[1] W. B. Bonnor, Null hypersurfaces in Minkowski space-time, Tensor (N.S.) 24 (1972), 329–345. Search in Google Scholar
[2] C. Călin, Contribution to geometry of CR-submanifold, Ph.D. thesis, University of Iasi, Romania, 1998. Search in Google Scholar
[3] K. L. Dugall and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Math. Appl. 364, Kluwer Academic, Dordrecht, 1996. 10.1007/978-94-017-2089-2Search in Google Scholar
[4] K. L. Duggal and D. H. Jin, Null Curves and Hypersurfaces of Semi-Riemannian Manifolds, World Scientific, Hackensack, 2007. 10.1142/6449Search in Google Scholar
[5] K. L. Duggal and D. H. Jin, A classification of Einstein lightlike hypersurfaces of a Lorentzian space form, J. Geom. Phys. 60 (2010), no. 12, 1881–1889. 10.1016/j.geomphys.2010.07.005Search in Google Scholar
[6] K. L. Dugall and B. Sahin, Differential Geometry of Lightlike Submanifolds, Front. Math., Birkhäuser, Basel, 2010. 10.1007/978-3-0346-0251-8Search in Google Scholar
[7] D. H. Jin, Screen conformal Einstein lightlike hypersurfaces of a Lorentzian space form, Commun. Korean Math. Soc. 25 (2010), no. 2, 225–234. 10.4134/CKMS.2010.25.2.225Search in Google Scholar
[8] D. H. Jin, Screen conformal lightlike real hypersurfaces of an indefinite complex space form, Bull. Korean Math. Soc. 47 (2010), no. 2, 341–353. 10.4134/BKMS.2010.47.2.341Search in Google Scholar
[9] 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 Appl. Math. 34 (2003), no. 9, 1369–1380. Search in Google Scholar
[10] T. H. Kang and S. K. Kim, Lightlike hypersurfaces of indefinite cosymplectic manifolds, Int. Math. Forum 2 (2007), no. 65–68, 3303–3316. 10.12988/imf.2007.07304Search in Google Scholar
[11] D. N. Kupeli, Singular Semi-Riemannian Geometry, Math. Appli. 366, Kluwer Academic, Dordrecht, 1996. 10.1007/978-94-015-8761-7Search in Google Scholar
[12] G. D. Ludden, Submanifolds of cosymplectic manifolds, J. Differential Geom. 4 (1970), 237–244. 10.4310/jdg/1214429387Search in Google Scholar
[13] B. O’Neill, Semi-Riemannian Geometry, Pure Appl. Math. 103, Academic Press, New York, 1983. Search in Google Scholar
[14] R. Roşca, On null hypersurfaces of a Lorentzian manifold, Tensor (N.S.) 23 (1972), 66–74. Search in Google Scholar
[15] A. Upadhyay and R. S. Gupta, Lightlike hypersurfaces of indefinite cosymplectic manifolds with parallel symmetric bilinear forms, Novi Sad J. Math. 40 (2010), no. 2, 37–45. Search in Google Scholar
[16] A. Upadhyay and R. S. Gupta, Semi-parallel lightlike hypersurfaces of indefinite cosymplectic space forms, Publ. Inst. Math. (Beograd) (N.S.) 89(103) (2011), 69–75. 10.2298/PIM1103069USearch in Google Scholar
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Articles in the same Issue
- Frontmatter
- Existence of solutions for Riemann–Liouville multi-valued fractional boundary value problems
- On certain subclasses of meromorphic univalent functions associated with a differential operator
- The normality criteria for families of entire algebroid functions
- Symmetric convergence of double series whose coefficients are the quotients of divisions of complex Fourier coefficients by their indexes
- On non-optimal spectral factorizations
- Hardy-type integral inequalities for quasi-monotone functions
- Certain results concerning operators on a Lie algebra and double index sequences
- The stability of some generalizations of the quadratic and Wilson’s functional equations
- Positive solutions of nonlinear fractional differential equations in non-zero self-distance spaces
- Dynamic contact problem with thermal effect
- Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold
- Closed range weighted composition operators on weighted Bergman spaces
- Two-weighted norm inequalities of singular integral operators on weighted Morrey spaces
Articles in the same Issue
- Frontmatter
- Existence of solutions for Riemann–Liouville multi-valued fractional boundary value problems
- On certain subclasses of meromorphic univalent functions associated with a differential operator
- The normality criteria for families of entire algebroid functions
- Symmetric convergence of double series whose coefficients are the quotients of divisions of complex Fourier coefficients by their indexes
- On non-optimal spectral factorizations
- Hardy-type integral inequalities for quasi-monotone functions
- Certain results concerning operators on a Lie algebra and double index sequences
- The stability of some generalizations of the quadratic and Wilson’s functional equations
- Positive solutions of nonlinear fractional differential equations in non-zero self-distance spaces
- Dynamic contact problem with thermal effect
- Screen conformal lightlike hypersurfaces of an indefinite cosymplectic manifold
- Closed range weighted composition operators on weighted Bergman spaces
- Two-weighted norm inequalities of singular integral operators on weighted Morrey spaces
