Riemannian geometry

Definitions

  • WordNet 3.6
    • n Riemannian geometry (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle "Bernhard Riemann pioneered elliptic geometry"
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Usage


In news:

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry )--the study of a smooth manifold furnished with a metric tensor of arbitrary signature.
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In science:

Some basic concepts and tools of non riemannian geometry in the frame-independent formalism are reviewed in sect. 2.
On the solutions of the Cartan equation in Metric Affine Gravity
This is obtained by formulating the non-Riemannian geometry in the frame independent approach.
On the solutions of the Cartan equation in Metric Affine Gravity
D∂i ∂j = Xk We are already in the position to state the “Fundamental Lemma of (pseudo)-Riemannian Geometry” in our setting.
Nonlinear distributional geometry and general relativity
We prove a “Fundamental Lemma of (pseudo-) Riemannian geometry” in this setting and define the notion of geodesics of a generalized metric.
Generalized pseudo-Riemannian geometry
The aim of this section is to initiate a study of pseudo-Riemannian geometry in the present setting.
Generalized pseudo-Riemannian geometry
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