# Riemannian

## Definitions

• WordNet 3.6
• adj Riemannian of or relating to Riemann's non-Euclidean geometry
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Century Dictionary and Cyclopedia
• riemannian Pertaining to Georg Friedrich Bernhard Riemann (1826–66), a noted German mathematician. Also written Riemannean.
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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:

Thus, if V is not Riemannian on M , we can ﬁnd an open subset U of M on which V is not Riemannian and H is integrable.
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
V is Riemannian on some open subset of M ; hence, by Proposition 1.4 , V is Riemannian on (M , g ) .
Harmonic morphisms with one-dimensional fibres on Einstein manifolds
Let X be the Riemannian universal covering of a compact Riemannian manifold M = X/Γ and {H ω = ∆ + V ω }ω∈Ω be a family of Schr¨odinger operators, parameterized by elements of the probability space (Ω, A, P).
Integrated density of states for ergodic random Schr\"odinger operators on manifolds
Let X be the Riemannian universal covering of a compact Riemannian manifold M = X/Γ and assume that Γ is of polynomial growth.
Integrated density of states for ergodic random Schr\"odinger operators on manifolds
Let X be the Riemannian universal covering of a compact Riemannian manifold M = X/Γ.
Integrated density of states for ergodic random Schr\"odinger operators on manifolds
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