Riemannian submanifold
Encyclopedia
A Riemannian submanifold N of a Riemannian manifold
M is a submanifold
of M equipped with the Riemannian metric inherited from M. The image of an isometric immersion is a Riemannian submanifold.
Riemannian manifold
In Riemannian geometry and the differential geometry of surfaces, a Riemannian manifold or Riemannian space is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, which varies smoothly from point to point...
M is a submanifold
Submanifold
In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required...
of M equipped with the Riemannian metric inherited from M. The image of an isometric immersion is a Riemannian submanifold.