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Constant scalar curvature and warped product globally null manifolds. (English) Zbl 1025.53040
The author describes an infinite family of light-like warped products of the form $M= L \times b \times_f F$ ($B$ being a Riemann surface and $F=(a, b)$ -- an open interval) of dimension $4$ and constant scalar curvature.

53C50Lorentz manifolds, manifolds with indefinite metrics
53B30Lorentz metrics, indefinite metrics
53C20Global Riemannian geometry, including pinching
Full Text: DOI
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[2] Anderson, M. T.: On the structure of solutions to the static vacuum Einstein equations. Ann. henri Poincarè 1, 977-994 (2000) · Zbl 1005.53055
[3] J.K. Beem, P.E. Ehrlich, K.L. Easley, Global Lorentzian Geometry, 2nd Edition, Marcel Dekker, New York, 1996.
[4] A. Besse, Einstein Manifolds, Springer, New York, 1987.
[5] Bishop, R. L.; O’neill, B.: Manifolds of negative curvature. Trans. am. Math. soc. 145, 1-49 (1969) · Zbl 0191.52002
[6] Dobarro, F.; Dozo, E. L.: Scalar curvature and warped products of Riemannian manifolds. Trans. am. Math. soc. 303, 161-168 (1987) · Zbl 0625.53043
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[8] K.L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Vol. 364, Kluwer Academic Publishers, Dordrecht, 1996. · Zbl 0848.53001
[9] Ehrlich, P. E.; Jung, Y. T.; Kim, S. B.: Constant curvatures on some warped product manifolds. Tsukuba J. Math. 20, No. 1, 239-256 (1996) · Zbl 0893.53016
[10] Kazdan, J. L.; Warner, F. W.: Scalar curvature and conformal deformation of Riemannian structure. J. diff. Geom. 10, 113-134 (1975) · Zbl 0296.53037
[11] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
[12] Yamabe, H.: On a deformation of Riemannian structures on compact manifolds. Osaka math. J. 12, 21-37 (1960) · Zbl 0096.37201