- In
differential geometry, a
Riemannian manifold is a
geometric space on
which many
geometric notions such as distance, angles, length, volume, and curvature...
-
Riemannian geometry is the
branch of
differential geometry that
studies Riemannian manifolds,
defined as
smooth manifolds with a
Riemannian metric (an...
- Sub-Riemannian
manifold Riemannian submanifold Riemannian metric Riemannian circle Riemannian submersion Riemannian Penrose inequality Riemannian holonomy Riemann...
- In
mathematical physics, a pseudo-
Riemannian manifold, also
called a semi-
Riemannian manifold, is a
differentiable manifold with a
metric tensor that is...
-
Riemannian manifolds. It ****igns a
tensor to each
point of a
Riemannian manifold (i.e., it is a
tensor field). It is a
local invariant of
Riemannian metrics...
- Neo-
Riemannian theory is a
loose collection of
ideas present in the
writings of
music theorists such as
David Lewin,
Brian Hyer,
Richard Cohn, and Henry...
- In mathematics, a
symmetric space is a
Riemannian manifold (or more generally, a pseudo-
Riemannian manifold)
whose group of
isometries contains an inversion...
- distance, shape, volume, or
other rigidifying structure. For example, in
Riemannian geometry distances and
angles are specified, in
symplectic geometry volumes...
-
examples include:
holonomy of the Levi-Civita
connection in
Riemannian geometry (called
Riemannian holonomy),
holonomy of
connections in
vector bundles, holonomy...
-
shortest path (arc)
between two
points in a surface, or more
generally in a
Riemannian manifold. The term also has
meaning in any
differentiable manifold with...
