| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4606580 | Differential Geometry and its Applications | 2010 | 8 Pages |
Abstract
The total curvature of C2C2 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. Castrillón López, V. Fernández Mateos, J. Muñoz Masqué,