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Generalization of p-regularity notion and tangent cone description in the singular case

Wiesław Grzegorczyk, Beata Medak, Alexey A. Tret’yakov (2012)

Annales UMCS, Mathematica

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.

Generalized Weingarten surfaces

Mohamed Afwat (1977)

Czechoslovak Mathematical Journal

Geodesics on the Ellipsoid.

Horst Knörrer (1980)

Inventiones mathematicae

Geometric mean curvature lines on surfaces immersed in $𝐑^{3}$

Ronaldo Garcia, Jorge Sotomayor (2002)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Geometrical considerations for ruling over the distribution of intensity of illumination on a skew ruled surface

Eberhard Meinicke (1984)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Geometrie und Geodäsie

Z. Nádeník (1989)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Geometry of the rolling ellipsoid

Krzysztof Andrzej Krakowski, Fátima Silva Leite (2016)

Kybernetika

We study rolling maps of the Euclidean ellipsoid, rolling upon its affine tangent space at a point. Driven by the geometry of rolling maps, we find a simple formula for the angular velocity of the rolling ellipsoid along any piecewise smooth curve in terms of the Gauss map. This result is then generalised to rolling any smooth hyper-surface. On the way, we derive a formula for the Gaussian curvature of an ellipsoid which has an elementary proof and has been previously known only for dimension two....