Glossary of Riemannian and Metric Geometry - N

N

Natural parametrization is the parametrization by length.

Net. A sub set S of a metric space X is called -net if for any point in X there is a point in S on the distance . This is distinct from topological nets which generalise limits.

Nilmanifold: An element of the minimal set of manifolds which includes a point, and has the following property: any oriented -bundle over a nilmanifold is a nilmanifold. It also can be defined as a factor of a connected nilpotent Lie group by a lattice.

Normal bundle: associated to an imbedding of a manifold M into an ambient Euclidean space, the normal bundle is a vector bundle whose fiber at each point p is the orthogonal complement (in ) of the tangent space .

Nonexpanding map same as short map