Explore: Global Riemannian Geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds. An example of a Riemannian manifold is a surface, on which

theorems of Riemannian geometry can be generalized to the pseudo-Riemannian case. In particular, the fundamental theorem of Riemannian geometry is true of

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

example, in Riemannian geometry distances and angles are specified, in symplectic geometry volumes may be computed, in conformal geometry only angles

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

metric is a Riemannian manifold, one with an indefinite metric is a pseudo-Riemannian manifold. Thus, isometries are studied in Riemannian geometry. A local

differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object that is determined by a choice of Riemannian or pseudo-Riemannian

tensors). Symplectic geometry has a number of similarities with and differences from Riemannian geometry. Unlike in the Riemannian case, symplectic manifolds

precise theorem of differential geometry and geometric analysis, in which physical systems are modeled by Riemannian manifolds with nonnegativity of a

sometimes termed Möbius geometry, and is a type of Klein geometry. A conformal manifold is a Riemannian manifold (or pseudo-Riemannian manifold) equipped with