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Geometric invariants and principal configurations on spacelike surfaces immersed in ℝ3,1

Published online by Cambridge University Press:  08 December 2010

Pierre Bayard  and
Federico Sánchez-Bringas
Pierre Bayard
Affiliation:
Instituto de Física y Matemáticas, U.M.S.N.H. Ciudad Universitaria, C.P. 58040 Morelia, Michoacán, Mexico ([email protected])
Federico Sánchez-Bringas
Affiliation:
Facultad de Ciencias, Departamento de Matemáticas, Circuito Exterior Cd. Universitaria, Colonia Copilco el Bajo, Delegación Coyoacán, Mexico D.F., C.P. 04510, Mexico ([email protected])
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Abstract

We describe the numerical invariants and the curvature ellipse attached to the second fundamental form of a spacelike surface in a four-dimensional Minkowski space. We then study the configuration of the V-principal curvature lines on a spacelike surface when the normal field V is lightlike (the lightcone configuration). We end with some observations on the mean directionally curved lines and on the asymptotic lines on spacelike surfaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 6 , December 2010 , pp. 1141 - 1160
Copyright
Copyright © Royal Society of Edinburgh 2010

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