(Carl Friedrich Gauss and Pierre Ossian Bonnet) Given a two-dimensional compact Riemannian manifold with boundary, Gaussian curvature of points and geodesic curvature of points on the boundary , it is the case that
where is the Euler characteristic of the manifold, denotes the measure with respect to area, and denotes the measure with respect to arclength on the boundary. This theorem expresses a topological invariant in terms of geometrical information.
|Date of creation||2013-03-22 16:36:37|
|Last modified on||2013-03-22 16:36:37|
|Last modified by||rspuzio (6075)|