Families of Gauss indicatrices on smooth surfaces in pseudo-spheres in the Minkowski 4-space

Farid Tari

Journal of Singularities
volume 1 (2010), 116-133

Received 13 April 2010. Received in revised form 9 August 2010.

DOI: 10.5427/jsing.2010.1h

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Abstract:

We study families of Gauss indicatrices on surfaces in pseudo-spheres in the Minkowski 4-space and obtain the generic local models of the configurations of the foliations determined by the fibres of their principal curvatures functions.

Keywords:

Binary differential equations, Gauss indicatrices, hyperbolic space, Minkowski space, spacelike surfaces, singularities, de Sitter space, timelike surfaces, versal unfoldings

Mathematical Subject Classification:

53A35, 53B30, 58K05, 34A09

Author(s) information:

Farid Tari
Department of Mathematical Sciences
Durham University, Science Laboratories
South Road, Durham DH1 3LE, UK
email: farid.tari@durham.ac.uk