Riemannian geometry

In differential geometry, the Laplace operator, named after Pierre-Simon Laplace, can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds.

In differential geometry, a geodesic (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) is a generalization of the notion of a "straight line" to "curved spaces".

A great circle, also known as an orthodrome or Riemannian circle, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold M equipped with an inner product on the tangent space at each point that varies smoothly from point to point in the sense that if X and Y are vector fields on M, then is a smooth function.

In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them.

In differential geometry, the Ricci flow (/ˈriːtʃi/) is an intrinsic geometric flow.

In mathematics, a conformal map is a function that preserves angles locally.

The shape of the universe is the and of the Universe, in terms of both curvature and topology (though, strictly speaking, the concept goes beyond both).

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.

In mathematics, a Hermitian symmetric space is a Hermitian manifold which at every point has as an inversion symmetry preserving the Hermitian structure.

In mathematics, constant curvature is a concept from differential geometry.

In mathematics, a Hermitian connection , is a connection on a Hermitian vector bundle over a smooth manifold which is compatible with the Hermitian metric.