A NOTE ON LORENTZIAN METRICS OF 3-DIMENSIONAL CONFORMALLY FLAT MANIFOLDS

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概要

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• In a Lorentzian manifold the backwards triangle inequality holds. This fact is confusing to our intuition. In the study of Lorentzian manifolds, Riemannian metrics are often used. But the relation between the Lorentzian metrics and the Riemannian metrics are not clear in most cases. In this note we see that there are examples of Riemannian manifolds the Riemannian metrics of which are closely related to the Lorentzian metrics defined on them. Specifically, we introduce a Lorentzian metric on a 3-dimensional pseudo-symmetric space (M, g) of constant type. If M is, furthermore, locally conformally flat, we see that the connection of the Lorentzian metric coincides with the Riemannian connection of g and hence we have the relations of their curvatures.

• 福岡工業大学の論文
• 2006-02-28

著者

• Goto Midori

  Department Of Computer And Systems Engineering Fukuoka Institute Of Technology

関連論文

• A NOTE ON LORENTZIAN METRICS OF 3-DIMENSIONAL CONFORMALLY FLAT MANIFOLDS
• Density theorems for invariant closed geodesics of a compact Riemannian manifold with strictly negative curvature

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