A classfication of 3-type curves in Minkowski 3-space . II.
A classification of 3-type curves in Minkowski 3-space . I.
A classification of 3-type curves in Minkowski 3-space e_1^3, II
A common characterization of the curvature axis for ruled surfaces and curves. (Eine gemeinsame Kennzeichnung der Krümmungsachse bei Regelflächen und Kurven.)
A four-vertex theorem for space curves.
A generalization of Frenet's frame for non-degenerate quadratic forms with any index
A geometric problem and the Hopf Lemma. I
A classical result of A. D. Alexandrov states that a connected compact smooth -dimensional manifold without boundary, embedded in , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of in a hyperplane in case satisfies: for any two points , on , with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for . Some variations...
A lower estimate for the number of zero-torsion points of a space curve.
A measure of symmetry for ovals
A new approach for describing instantaneous line congruence
Based on the E. Study’s map, a new approach describing instantaneous line congruence during the motion of the Darboux frame on a regular non-spherical and non-developable surface, whose parametric curves are lines of curvature, is proposed. Afterward, the pitch of general line congruence is developed and used for deriving necessary and sufficient condition for instantaneous line congruence to be normal. In terms of this, the derived line congruences and their differential geometric invariants were...
A non-standard approach to the Euclidean study of plane curves.
A Note Concerning a Statement of Hollcroft.
A note on ovals and their evolutoides.
A note on secantoptics.
A singular example for the averaged mean curvature flow.
A Software for the Visualisationof Differential Geometry
A spherical Fabricius-Bjerre formula with applications to closed space curves.
Affine classification of -curves.
Affine invariants of annuli
A family of regular annuli is considered. Affine invariants of annuli are introduced.
Affinely invariant symmetry sets
The classical medial axis and symmetry set of a smooth simple plane curve M, depending as they do on circles bitangent to M, are invariant under euclidean transformations. This article surveys the various ways in which the construction has been adapted to be invariant under affine transformations. They include affine distance and area constructions, and also the 'centre symmetry set' which generalizes central symmetry. A connexion is also made with the tricentre set of a convex plane curve, which...