Singularities of Gauss maps of wave fronts with non-degenerate singular points

We study singularities of Gauss maps of (wave) fronts and give characterizations of singularities of Gauss maps by geometric properties of fronts which are related to behavior of bounded principal curvatures. Moreover, we investigate the relation between a kind of boundedness of Gaussian curvatures near cuspidal edges and types of singularities of their Gauss maps. Further, we consider extended height functions on fronts with non-degenerate singular points.

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Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).