Warped Product Lightlike Submanifolds
DOI:
https://doi.org/10.5644/SJM.01.2.10Keywords:
Degenerate metric, warped product manifold, semi-Riemann manifoldAbstract
e study a new class of lightlike submanifolds $M$, called warped product lightlike submanifolds, of a semi-Riemann manifold. We show that the null geometry of $M$ reduces to the corresponding non-degenerate geometry of its semi-Riemann submanifold.
2000 Mathematics Subject Classification. 53C15, 53C40, 53C50
Downloads
References
C. Atindogbe and K. L. Duggal, Conformal screen on lightlike hypersurfaces, Int. J. Pure Appl. Math., 11 (4) (2004), 421–442.
A. Bejancu, Null hypersurfaces of semi-Euclidean spaces, Saitama Math. J., 14 (1996), 25–40.
A. Bejancu, A. Ferr´andez and P. Lucas, A new viewpoint on geometry of a lightlike hypersurface in a semi-Euclidean space, Saitama Math. J., 16 (1998), 31–38.
R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1–49.
K. L. Duggal, Constant scalar curvature and warped product globally null manifolds, J. Geom. Phys., 4 (2002), 327–340.
K. L. Duggal, Riemannian geometry of half-lightlike manifolds, Math. J. Toyama Univ., 25 (2002), 165–179.
K. L. Duggal and A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Its Applications, Kluwer Academic Publishers, Dortrecht, (1996).
K. L. Duggal and D. H. Jin, Totally umbilical lightlike submanifolds, Kodai Math J., 26 (2003), 49–68.
K. L. Duggal and B. Sahin, Screen conformal half-lightlike submanifolds, Internat J. Math. and Math. Sci., 68 (2004), 3737–3753.
B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, (1983).
