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Results tagged with dg.differential-geometry
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user 27446
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
1
answer
308
views
Generalization of Vogt's Theorem for curves in higher dimension
The Vogt's theorem for plane curves states that if A and B are endpoints of a spiral arc,
the curvature nondecreasing from A to B. The angle $\beta$ of the tangent to the arc at B with the chord AB …
1
vote
Generalization of Vogt's Theorem for curves in higher dimension
This is an attempt at an (as yet incomplete) proof of the above claim. I would be happy to receive any corrections and/or comments.
Let us denote the curve $\gamma$ by the following parametrization …
2
votes
1
answer
420
views
Characterization of convex space curve
In general, a smooth curve $C$ in $R^3$ that lies entirely on the boundary of its convex hull, $\mathcal{H}(C)$, is defined to be convex.
Does any one know of a characterization of a curve in space …