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Results tagged with riemannian-geometry
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user 494523
Riemannian Geometry is a subfield of Differential Geometry, which specifically studies "Riemannian Manifolds", manifolds with "Riemannian Metrics", which means that they are equipped with continuous inner products.
0
votes
Compute Christoffel symbols of sphere by embedding
I want to further explain why I care about this issue. I want to compute curvature by embedding.
Consider $\{x_{n+1}>0 \}$
\begin{equation*}
\left\{\begin{aligned}
& y_1=x_1\\
&\vdots \\
…
- 21
2
votes
2
answers
213
views
Compute Christoffel symbols of sphere by embedding
In his answer V. Semeria, starts by taking
$$(y_1,\dots,y_{n+1})=\left(x_1,\dots,x_n,\sum_{i=1}^{n+1}x_i^2 -R^2\right)$$
Write $(\vec{e}_1,\dots,\vec{e}_{n+1})$ the canonical basis of $\mathbb{R}^{n+1 …
- 21