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A surface that contains many Lorentzian circles

Part of: Local differential geometry Global differential geometry

Published online by Cambridge University Press:  30 April 2010

Graciela S. Birman  and
Graciela M. Desideri
Graciela S. Birman
Affiliation:
Núcleo Consolidado de Matemática Pura y Aplicada (NUCOMPA), Facultad de Ciencias Exacta, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, 7000 Tandil, Argentina ([email protected]; [email protected])
Graciela M. Desideri
Affiliation:
Núcleo Consolidado de Matemática Pura y Aplicada (NUCOMPA), Facultad de Ciencias Exacta, Universidad Nacional del Centro de la Provincia de Buenos Aires, Pinto 399, 7000 Tandil, Argentina ([email protected]; [email protected])
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Abstract

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The characterization of a surface by means of the circles contained in it has been studied by S. Izuyima, A. Takiyama, K. Ogiu, R. Takagi and N. Takeuchi, among others. The aim of this paper is to show some characterizations of a pseudosphere in Lorentz 3-space, assuming the existence of Lorentzian and Euclidean circles.

Keywords

pseudosphereLorentzian spaceLorentzian circleEuclidean circle

MSC classification

Secondary: 53C50: Lorentz manifolds, manifolds with indefinite metrics 53B30: Lorentz metrics, indefinite metrics
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 293 - 298
Copyright
Copyright © Edinburgh Mathematical Society 2010