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Curvatures of conflict surfaces in Euclidean 3-space

Jorge Sotomayor, Dirk Siersma, Ronaldo Garcia (1999)

Banach Center Publications

This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane, established by Siersma [3]. In the present case a conflict surface arises, equidistant from the given convex sets. The Gaussian, mean curvatures and the location of umbilic points on the conflict surface are determined here. Initial results on the Darbouxian type of umbilic points on conflict surfaces are also established. The results are expressed in terms of the principal...

Curves and surfaces in hyperbolic space

Shyuichi Izumiya, Donghe Pei, Masatomo Takahashi (2004)

Banach Center Publications

In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.

Curves in Banach spaces which allow a C 1 , BV parametrization or a parametrization with finite convexity

Jakub Duda, Luděk Zajíček (2013)

Czechoslovak Mathematical Journal

We give a complete characterization of those f : [ 0 , 1 ] → X (where X is a Banach space) which allow an equivalent C 1 , BV parametrization (i.e., a C 1 parametrization whose derivative has bounded variation) or a parametrization with bounded convexity. Our results are new also for X = ℝ n . We present examples which show applicability of our characterizations. For example, we show that the C 1 , BV and C 2 parametrization problems are equivalent for X = ℝ but are not equivalent for X = ℝ 2 .

Curves with finite turn

Jakub Duda (2008)

Czechoslovak Mathematical Journal

In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness...

Darboux transforms of Dupin surfaces

Emilio Musso, Lorenzo Nicolodi (2002)

Banach Center Publications

We present a Möbius invariant construction of the Darboux transformation for isothermic surfaces by the method of moving frames and use it to give a complete classification of the Darboux transforms of Dupin surfaces.

Darboux-Zwangläufe und äquiforme Kinematik

Otto Röschel (1991)

Applications of Mathematics

In dieser Arbeit werden Yusammensetzungen euklidischer Darboux - Zwangläufe mit rastfesten zentrischen Ähnlichkeiten studiert. Bei den so entstehenden zweiparametrigen äquiformen Bewegungsvorgängen werden die Punkte einer besonderen gangfesten Fläche dritter Ordnung φ in Bahnebenen geführt, während allgemeine Punkte des Gangraumes an Kegel zweiter Ordnung gebunden sind. Weiters wird gezeigt, dass sich durch Spezialisierung innerhalb dieser zweiparametrigen Schar alle von A. Karger [2] angegeben...

Currently displaying 381 – 400 of 2174