A criterion for global hyperbolicity of left-invariant Lorentz metrics on Lie groups |
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Authors: | Mohammed Guediri |
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Institution: | Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia |
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Abstract: | We show that every left-invariant Lorentz metric on a non-abelian simply connected Lie group is globally hyperbolic whenever its restriction to the commutator ideal of the Lie algebra is positive definite. We also show that a left-invariant Lorentz metric on the three-dimensional Heisenberg group is globally hyperbolic if and only if its restriction to the center of the Lie algebra is positive definite or degenerate. |
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Keywords: | primary 53C50 83C75 17B81 |
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