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A Riemannian submanifold N {\displaystyle N} of a Riemannian manifold M {\displaystyle M} is a submanifold N {\displaystyle N} of M {\displaystyle M} equipped...

{\displaystyle (M,g)} be a Riemannian manifold and let i : N → M {\displaystyle i:N\to M} be an immersed submanifold or an embedded submanifold of M {\displaystyle...

Sub-Riemannian manifold Riemannian submanifold Riemannian metric Riemannian circle Riemannian submersion Riemannian Penrose inequality Riemannian holonomy Riemann...

topological obstructions. Furthermore, a submanifold does not always inherit the structure of a pseudo-Riemannian manifold; for example, the metric tensor...

charts List of formulas in Riemannian geometry Christoffel symbols Intrinsic metric Pseudo-Riemannian manifold Sub-Riemannian manifold Finsler geometry...

non-negatively curved n-dimensional Riemannian manifold, then M contains a compact, totally geodesic submanifold S such that M is diffeomorphic to the...

a formula for the Laplacian of the second fundamental form of a Riemannian submanifold. It is often quoted and used in the less precise form of a formula...

three-dimensional, space-like, totally geodesic submanifold of a (3 + 1)-dimensional spacetime. Such a submanifold is often called a time-symmetric initial data...

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following...

inequality Riemannian polyhedron Riemannian singular value decomposition Riemannian submanifold Riemannian submersion Riemannian volume form Riemannian wavefield...

cuspidal edge which switch from one sheet to the other. A point p in a Riemannian submanifold is umbilical if, at p, the (vector-valued) Second fundamental form...

subspace to a submanifold is co-isotropic (the dual of an isotropic subspace), the submanifold is called co-isotropic. Lagrangian submanifolds of a symplectic...

which give invariants of contact manifolds and their Legendrian submanifolds Sub-Riemannian geometry Hoffman, William C. (1989-08-01). "The visual cortex...

structure of an arbitrary submanifold tangent vector has an angle of k with the submanifold's tangent space. In Riemannian geometry, Chen and Kentaro...

In Riemannian geometry, an exponential map is a map from a subset of a tangent space TpM of a Riemannian manifold (or pseudo-Riemannian manifold) M to...

In Riemannian geometry, the geodesic curvature k g {\displaystyle k_{g}} of a curve γ {\displaystyle \gamma } measures how far the curve is from being...

, g ) {\displaystyle (M,g)} be a Riemannian manifold, and S ⊂ M {\displaystyle S\subset M} a Riemannian submanifold. Define, for a given p ∈ S {\displaystyle...

independently by Allendoerfer in 1939 and Fenchel in 1940 to a Riemannian submanifold of a Euclidean space of any codimension, for which they used the...

the set F − 1 ( y ) {\displaystyle \scriptstyle F^{-1}(y)} is a Riemannian submanifold of M {\displaystyle \scriptstyle M} , so the integrals in the right-hand...

curvature of hypersurfaces and submanifolds see second fundamental form, in coordinates see the list of formulas in Riemannian geometry or covariant derivative...