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Total Curvature of Curves in Riemannian Manifolds

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Castrillón López, Marco and Muñoz Masqué, Jaime and Fernández Mateos, Victor (2010) Total Curvature of Curves in Riemannian Manifolds. Differential Geometry and its Applications, 28 (2). pp. 140-147. ISSN 0926-2245

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Official URL: http://www.sciencedirect.com/science/journal/09262245


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Abstract

The total curvature of C2 curves embedded in an arbitrary Riemannian manifold is shown to be the limit of the curvatures of inscribed geodesic polygons. The formula for the total curvature of a curve as the least upper bound of curvatures of inscribed geodesic polygons holds for a manifold of non-positive sectional curvature only.


Item Type:Article
Uncontrolled Keywords:Geodesic Polygon; Total Curvature; Riemannian Manifold
Subjects:Sciences > Mathematics > Differential geometry
ID Code:21620
Deposited On:31 May 2013 14:32
Last Modified:12 Jun 2018 11:00

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