FOCAL SURFACES OF FRONTS ASSOCIATED TO UNBOUNDED PRINCIPAL CURVATURES

Keisuke Teramoto

doi:10.1216/rmj.2023.53.1587

Abstract

We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near nondegenerate singular points of initial fronts. We give characterizations of singularities of those focal surfaces in terms of types of singularities and geometrical properties of initial fronts. Moreover, we investigate behavior of the Gaussian curvature of the focal surface.

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Keisuke Teramoto. "FOCAL SURFACES OF FRONTS ASSOCIATED TO UNBOUNDED PRINCIPAL CURVATURES." Rocky Mountain J. Math. 53 (5) 1587 - 1608, October 2023. https://doi.org/10.1216/rmj.2023.53.1587

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Received: 1 March 2022; Accepted: 26 September 2022; Published: October 2023

First available in Project Euclid: 19 September 2023

MathSciNet: MR4643821

Digital Object Identifier: 10.1216/rmj.2023.53.1587

Subjects:

Primary: 53A05 , 53A55 , 57R45

Keywords: focal surface , front , Gaussian curvature , principal curvature , singularity , subparabolic point

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