The evolute of a curve, a surface, or more generally a submanifold, is the caustic of the normal map.
32.
Assume that the moment map is proper and that it achieves its maximum m exactly along a symplectic submanifold Z of X.
33.
On a dense open subset of the semialgebraic set " S ", it is ( locally ) a submanifold.
34.
Let f : X \ rightarrow Y be a smooth map between manifolds, and let Z be a submanifold of Y.
35.
The volume of 3D submanifold that contains part of spin network is given by a sum of contributions from each node inside it.
36.
The covariant derivative of a vector in a submanifold of a Riemannian manifold need not equal the induced covariant derivative of that vector.
37.
A submanifold is said to be umbilic ( or all-umbilic ) if this condition holds at every point " p ".
38.
A Lagrangian submanifold is, by definition, an isotropic submanifold of maximal dimension, namely half the dimension of the ambient symplectic manifold.
39.
A Lagrangian submanifold is, by definition, an isotropic submanifold of maximal dimension, namely half the dimension of the ambient symplectic manifold.
40.
In other words, an embedding is diffeomorphic to its image, and in particular the image of an embedding must be a submanifold.
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