On completeness in affine differential geometry

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1986 English Publisher:Springer Science and Business Media LLCJournal:Geometriae Dedicata, volume 20 (issn: 0046-5755, eissn: 1572-9168,

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Authors: Nomizu, Katsumi;

doi: 10.1007/bf00149271

On completeness in affine differential geometry

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Abstract

The author considers different notions of completeness in affine differential geometry. He gives an example of a spacelike surface M in \({\mathbb{R}}^ 3\), where \({\mathbb{R}}^ 3\) carries the Lorentz-Minkowski- metric, such that the induced metric on M is complete, but the equiaffine metric of M is not complete.

Related Organizations

Max Planck Society
Germany
Max Planck Institute for Mathematics
Germany

Keywords

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, completeness of connections, equiaffine metric, Affine differential geometry, spacelike surface, Linear and affine connections

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