The Conformal Pseudodistance and Null Geodesic Incompleteness

Details The Conformal Pseudodistance and Null Geodesic Incompleteness The Conformal Pseudodistance and Null Geodesic Incompleteness

2011-08-09

arxiv.org/abs/1108.1965v1

Mathematics

Differential Geometry

This is a short note on a result announced at the "Workshop on Cartan Connections, Geometry of Homogeneous Spaces, and Dynamic

Scientific paper

We clarify the relationship between the null geodesic completeness of an Einstein Lorentz manifold and its conformal Kobayashi pseudodistance. We show that an Einstein manifold has at least one incomplete null geodesic if its pseudodistancfe is nontrivial. If its pseudodistance is nondegenerate, all of its null geodesics must be incomplete. Thus an Einstein manifold (M,g) has no complete null geodesic if there is a "physical metric" in the conformal class of g satisfying the null convergence and null generic conditions.

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