Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleGeometry of timelike minimal surfaces and null curves
PresenterShintaro Akamine (Kyushu University)
Author(s)Mr Shintaro Akamine

Timelike surfaces in the 3-dimensional Lorentz-Minkowski space are surfaces with
non-degenerate index 1 metrics. In contrast to surfaces in the 3-dimensional
Euclidean space and spacelike surfaces in the Lorentz-Minkowski space, these
surfaces have not always principal curvatures, that is, their shape operators
are not always diagonalizable even over the complex field. For the case of
timelike minimal surfaces, the problem of the diagonalizability of the shape
operator is reduced to a problem of the sign of the Gaussian curvature. In this
talk, we determine the sign of the Gaussian curvature of a timelike minimal
surface from a viewpoint of null curves. Moreover, we also investigate the
behavior of a timelike minimal surface with some kind of singularities.