Extends the classical fundamental theorem of surface theory to proper frontals, singular surfaces with empty interior singular set, using a moving-base decomposition and characterizing wave fronts via new relative curvatures.
Recognition Problem of Frontal Singularities
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abstract
This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the recognition results by K. Saji and several arguments on openings, which was performed for the classification of singularities of tangent surfaces (tangent developables) by the author. As an application of our solutions of recognition problem of frontal singularities, we announce the classification of singularities appearing in tangent surfaces of generic null curves which are ruled by null geodesics in general Lorentz three-manifolds, mentioning related recognition results and open problems.
fields
math.DG 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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The fundamental theorem for singular surfaces with limiting tangent planes
Extends the classical fundamental theorem of surface theory to proper frontals, singular surfaces with empty interior singular set, using a moving-base decomposition and characterizing wave fronts via new relative curvatures.