Metrics in the space of curves
نویسنده
چکیده
In this paper we study geometries on the manifold of curves. We define a manifold M where objects c ∈ M are curves, which we parameterize as c : S → lR (n ≥ 2, S is the circle). Given a curve c, we define the tangent space TcM of M at c including in it all deformations h : S → lR of c. We discuss Riemannian and Finsler metrics F (c, h) on this manifold M , and in particular the case of the geometric H metric F (c, h) = ∫ |h|ds of normal deformations h of c; we study the existence of minimal geodesics of H under constraints; we moreover propose a conformal version of the H metric.
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