$H^{o}$-type Riemannian metrics on the space of planar curves
نویسندگان
چکیده
منابع مشابه
H-type Riemannian Metrics on the Space of Planar Curves
Michor and Mumford have shown that the distances between planar curves in the simplest metric (not involving derivatives) are identically zero. We derive geodesic equations and a formula for sectional curvature for conformally equivalent metrics. We show if the conformal factor depends only on the length of the curve, the metric behaves like an L metric, the sectional curvature is not bounded f...
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Michor and Mumford have shown that the distances between planar curves in the simplest metric (not involving derivatives) are identically zero. We consider two conformally equivalent metrics for which the distances between curves are nontrivial. We show that in the case of the simpler of the two metrics, the only minimal geodesics are those corresponding to curve evolution in which the points o...
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متن کاملAn H type Riemannian metric on the space of planar curves
An H type metric on the space of planar curves is proposed and equation of the geodesic is derived. A numerical example is given to illustrate the differneces between H and H metrics.
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An H type metric on the space of planar curves is proposed and equation of the geodesic is derived. A numerical example is given to illustrate the differneces between H and H metrics.
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ژورنال
عنوان ژورنال: Quarterly of Applied Mathematics
سال: 2007
ISSN: 0033-569X,1552-4485
DOI: 10.1090/s0033-569x-07-01084-4