Duggal, K. L. On scalar curvature in light-like geometry. (English) Zbl 1107.53047 J. Geom. Phys. 57, No. 2, 473-481 (2007). Summary: We introduce the concept of induced scalar curvature of a class \({\mathcal C}[M]\), of light-like hypersurfaces \((M,g,S(TM))\), of a Lorentzian manifold, such that \(M\) admits a canonical screen distribution \(S(TM)\), a canonical light-like transversal vector bundle and an induced symmetric Ricci tensor. We prove that there exists such a class \({\mathcal C}[M]\) of a globally hyperbolic warped product space-time [J. K. Beem, P. E. Ehrlich, and K. L. Easley, Global Lorentzian Geometry, 2nd edition, Marcel Dekker, Inc. New York (1996; Zbl 0846.53001)] of general relativity. In particular, we calculate the scalar curvature of a member of \({\mathcal C}[M]\) in a globally hyperbolic space-time of constant curvature, supported by an example. Cited in 16 Documents MSC: 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 53C20 Global Riemannian geometry, including pinching 53B50 Applications of local differential geometry to the sciences Keywords:degenerate metric; Riemannian screen distribution; scalar curvature Citations:Zbl 0846.53001 PDFBibTeX XMLCite \textit{K. L. Duggal}, J. Geom. Phys. 57, No. 2, 473--481 (2007; Zbl 1107.53047) Full Text: DOI References: [1] Akivis, M. A.; Goldberg, V. V., The geometry of lightlike hypersurfaces of the de sitter space, Acta Appl. Math., 53, 297-328 (1998), MR 1653456 (2000c:53086) · Zbl 0921.53008 [2] Barros, M.; Romero, A., Indefinite Kaehler manifolds, Math. Ann., 261, 55-62 (1982), MR 0675207 (84d: 53033) · Zbl 0476.53013 [3] Beem, J. K.; Ehrlich, P. E.; Easley, K. L., Global Lorentzian Geometry (1996), Marcel Dekker, Inc.: Marcel Dekker, Inc. New York, MR1384756 (97f:53100) [4] Bonnor, W. B., Null hypersurfaces in Minkowski spacetime, Tensor (N.S.), 20, 329-345 (1972), MR 0334047 (48: 12366) · Zbl 0233.53010 [5] Duggal, K. L., Constant scalar curvature and warped product globally null manifolds, J. Geom. Phys., 43, 4, 327-340 (2002), MR 1929910 (2004b:53122) · Zbl 1025.53040 [6] Duggal, K. L.; Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, vol. 364 (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, MR1383318 (97e:53121) [7] Duggal, K. L.; Giménez, A., Lightlike hypersurfaces of Lorentzian manifolds with distinguished screen, J. Geom. Phys., 55, 107-122 (2005), MR 2157417 (2006 b: 53072) · Zbl 1111.53029 [8] Galloway, G. J., Maximum principles for null hypersurfaces and null splitting theorems, Ann. Henri Poincaré, 1, 543-567 (2000), MR 1777311 (2002b:53052) · Zbl 0965.53048 [9] Kupeli, D. N., Singular Semi-Riemannian Geometry, vol. 366 (1996), Kluwer Acad. Publishers: Kluwer Acad. Publishers Dordrecht, MR 1392222 (97f: 53105) · Zbl 0871.53001 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.