The fibre bundle of degenerate tangent planes of a Lorentzian manifold and the smoothness of the null sectional curvature |
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Authors: | Francisco J Palomo |
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Institution: | Departamento de Matemática Aplicada, Universidad de Málaga, Complejo Tecnológico, Campus Teatinos, 29071-Málaga, Spain |
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Abstract: | The Grassmann bundle of degenerate tangent planes to a Lorentzian manifold is introduced and several of its properties are deduced. After a suitable normalization, the null sectional curvature associated to a Lorentzian metric may be considered as a well-defined function on the Grassmann bundle of degenerate tangent planes. The smoothness of this function is proved and some consequences are obtained. |
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Keywords: | 53C50 |
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