Kyushu Journal of Mathematics
Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116
WEAKLY COMPLETE WAVE FRONTS WITH ONE PRINCIPAL CURVATURE CONSTANT
Atsufumi HONDA
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2016 Volume 70 Issue 2 Pages 217-226

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Abstract

Murata and Umehara gave a classification of complete flat fronts in the Euclidean 3-space and proved their orientability. Here, a flat front is a flat surface (i.e., a surface where one of the principal curvatures is identically zero) with admissible singularities. In this paper,we investigate wave fronts where one of the principal curvatures is a non-zero constant. Although they are orientable in the regular surface case, there exist non-orientable examples. We classify weakly complete ones and derive their orientability.

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© 2016 Faculty of Mathematics, Kyushu University
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