Riemannian

Geometry, defining it as a duality between a general manifold and a so-called Riemannian metric.

SPACE SALOMON BOCHNER 1968

“Habilitationsschrift” (1868); and as an immediate ap - plication of it he outlined the so-called Riemannian

SPACE SALOMON BOCHNER 1968

Life as it exists at any point in physical-space-time, is a finite domain, but, by virtue of what were usefully identified as Riemannian evolution, is not a bounded domain.

LaRouche's Latest 2009

This qualification is, that all competent modern science is Riemannian in that coincidental sense of the use of the term "Riemannian" by both Einstein's treatment of the subject of Kepler's astronomy, and in the related case of Academician V.I. Vernadsky's defining of the physical chemistry of the Noösphere.

LaRouche's Latest 2009

Some informal background: a Riemannian manifold is a differentiable manifold (where the tangent space at each point has an inner product) with a positive-definite metric tensor, d (x, y) ≥ 0.

Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

A familiar Riemannian manifold is a Euclidean manifold (where one has to add a smoothly varying inner product on the tangent space of the standard Euclidean space), with the familiar Euclidean (distance) metric (our 3-space, for example).

Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

However, the General Theory of Relativity explains the concept of gravitation by using Riemannian geometry.

Matthew Yglesias » Cato’s David Boaz Joins George Will in Peddling Bogus “Global Cooling” Stories 2009

The Lorentzian manifold is a pseudo-Riemannian manifold, the generalization of the Riemannian manifold, such that the metric tensor need not be positive-definite.

Bad Language: Metric vs Metric Tensor vs Matrix Form vs Line Element 2009

“However, the General Theory of Relativity explains the concept of gravitation by using Riemannian geometry”

Matthew Yglesias » Cato’s David Boaz Joins George Will in Peddling Bogus “Global Cooling” Stories 2009

Riemannian writes: Bryan, have you noticed any more Ivory Tower academics more partial to blogging as a result of the increasingly prominent stature of the GMU economics department on the blogosphere, especially with the attention yours 'and Tyler's books are receiving?

Nominal Rigidities and the Law of One Price Break Down, Bryan Caplan | EconLog | Library of Economics and Liberty 2009