Lorentzian Clairaut submersions |
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Authors: | Dean Allison |
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Institution: | (1) Department of Mathematical Sciences, University of Northern Colorado, 80639 Greeley, CO, USA |
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Abstract: | We investigate a class of semi-Riemannian submersions satisfying a Lorentzian analogue of the classical Clairaut's relation for surfaces of revolution. We show that a Lorentzian submersion with one-dimensional fibers is Clairaut if and only if the fibers are totally umbilic with a gradient field as the normal curvature vector field. We also investigate the behavior of timelike and null geodesics in Lorentzian Clairaut submersions. In particular, every null geodesic of a Lorentzian Clairaut submersion with one-dimensional fibers projects to a pregeodesic in the base space with respect to a conformally related metric on the base space if and only if the integrability tensor of the submersion vanishes. |
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Keywords: | Primary 53C50 Secondary 53C22 |
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