Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds

Atsufumi Honda; Kentaro Saji; Keisuke Teramoto

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arXiv · 1811.11392

Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds

Atsufumi Honda·Kentaro Saji·Keisuke Teramoto

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Abstract

A mixed type surface is a connected regular surface in a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced metric of a mixed type surface is a signature-changing metric, and their lightlike points may be regarded as singular points of such metrics. In this paper, we investigate the behavior of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface. To characterize the boundedness of Gaussian curvature at a non-degenerate lightlike points, we introduce several fundamental invariants along non-degenerate lightlike points, such as the lightlike singular curvature and the lightlike normal curvature. Moreover, using the results by Pelletier and Steller, we obtain the Gauss-Bonnet type formula for mixed type surfaces with bounded Gaussian curvature.

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BibTeX RIS

Atsufumi Honda, Kentaro Saji, Keisuke Teramoto. 2018-11-28. Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds. https://arxiv.org/abs/1811.11392

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