### Some articles on *riemannian metric, metric, riemannian metrics, riemannian*:

Gauss–Bonnet Theorem - Interpretation and Significance

... If the torus carries the ordinary

... If the torus carries the ordinary

**Riemannian metric**from its embedding in R3, then the inside has negative Gaussian curvature, the outside has positive Gaussian curvature, and the total ... to construct a torus by identifying opposite sides of a square, in which case the**Riemannian metric**on the torus is flat and has constant curvature 0, again resulting in total curvature 0 ... It is not possible to specify a**Riemannian metric**on the torus with everywhere positive or everywhere negative Gaussian curvature ...Differential Geometry Of Surfaces - Local Metric Structure

... This structure is encoded infinitesimally in a

... This structure is encoded infinitesimally in a

**Riemannian metric**on the surface through line elements and area elements ... and early twentieth centuries only surfaces embedded in R3 were considered and the**metric**was given as a 2×2 positive definite matrix varying smoothly from point to point in a ... into account local distortions of the Earth's surface to calculate true distances, so the**Riemannian metric**describes distances and areas "in the small" in each ...Differential Geometry Of Surfaces - Overview

... Smooth surfaces equipped with

... Smooth surfaces equipped with

**Riemannian metrics**are of foundational importance in differential geometry ... A**Riemannian metric**endows a surface with notions of geodesic, distance, angle, and area ... on a closed oriented surface correspond to conformal equivalence classes of**Riemannian metrics**on the surface ...Contact Geometry - Contact Forms and Structures - Relation With Symplectic Structures

... Choose a

... Choose a

**Riemannian metric**on the manifold N and let H be the associated kinetic energy ... it generates the geodesic flow of the**Riemannian metric**... More precisely, using the**Riemannian metric**, one can identify each point of the cotangent bundle of N with a point of the tangent bundle of N, and then the value of R at that point of the (unit ...Pseudo-Riemannian Manifold

... A pseudo-

... A pseudo-

**Riemannian**manifold is a differentiable manifold equipped with a non-degenerate, smooth, symmetric**metric**tensor which, unlike a**Riemannian metric**, need not be positive-definite, but ... Such a**metric**is called a pseudo-**Riemannian metric**and its values can be positive, negative or zero ... The signature of a pseudo-**Riemannian metric**is (p, q) where both p and q are non-negative ...Main Site Subjects

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