Isometric deformations of mixed type surfaces in Lorentz-Minkowski space

2019/08/06 by Atsufumi Honda, Honda, Atsufumi · 1 citation
Mathematics · #35M10 #53A35 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53B30 #Secondary 57R45 #math.DG #msc:35M10 #msc:53A35 #msc:53B30 #msc:57R45

paper · pdf · doi:10.48550/arxiv.1908.01967

33 pages, 12 figures

arxiv created 2019/08/06 · arxiv updated 2019/08/07

Abstract

A connected regular surface in Lorentz-Minkowski 3-space is called a mixed type surface if the spacelike, timelike and lightlike point sets are all non-empty. Lightlike points on mixed type surfaces may be regarded as singular points of the induced metrics. In this paper, we introduce the L-Gauss map around non-degenerate lightlike points, and show the fundamental theorem of surface theory for mixed type surfaces at non-degenerate lightlike points. As an application, we prove that a real analytic mixed type surface admits non-trivial isometric deformations around generic lightlike points.

Cited by

• Behavior of Gauss curvatures and mean curvatures of Lightcone framed surfaces in the Lorentz-Minkowski 3-space

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