Definition:Euclidean Space/Riemannian Manifold
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Definition
Let $\struct {M, g}$ be a Riemannian manifold where $M = \R^n$ for some $n \in \N_{> 0}$ and $g$ is the Euclidean metric.
Then $\struct {M, g}$ is known as the ($n$-dimensional) Euclidean space.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 3$: Model Riemannian Manifolds. Euclidean Spaces