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Curvatures of conflict surfaces in Euclidean 3-space

100%

Sotomayor J., Siersma D., Garcia R.

Banach Center Publications

1999

tom 50

nr 1

277-285

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 directions and on the curvatures of the borders of the given convex sets.

Foliations making a constant angle with principal directions on ellipsoids

100%

Garcia R., Langevin R., Walczak P.

Annales Polonici Mathematici

2015

tom 113

nr 2

165-173

We study the global behavior of foliations of ellipsoids by curves making a constant angle with the lines of curvature.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Banach Center Publications

2 Garcia R.

1 Langevin R.

1 Siersma D.

1 Sotomayor J.

1 Walczak P.

1 2015

1 1999

Wyniki wyszukiwania

Curvatures of conflict surfaces in Euclidean 3-space

Foliations making a constant angle with principal directions on ellipsoids