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Results tagged with riemannian-geometry
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user 9456
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.
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Is Riemannian distance function equivalent to Euclidean one?
Consider the Riemannian manifold $\mathbb{R}^n$ and a smooth Riemannian metric $G:\mathbb{R}^n\rightarrow\mathbb{R}^{n\times{n}}$. We know that if $w_1I_n\leq{G}(x)\leq{w_2}I_n$ for some $w_1,w_2\in\m …
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When is the Riemannian manifold $\mathbb{R}^n$ complete as a metric space with respect to th...
Consider the Riemannian manifold $\mathbb{R}^n$ and a smooth Riemannian metric $G:\mathbb{R}^n\rightarrow\mathbb{R}^{n\times{n}}$. What is the minimum assumption on $G$ such that the manifold $\mathbb …
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Finding an appropriate Riemannian metric $G:\mathbb{R}^3\rightarrow\mathbb{R}^{3\times{3}}$ ...
I am trying to find a Riemannian metric $G:\mathbb{R}^3\rightarrow\mathbb{R}^{3\times{3}}$ on the manifold $\mathbb{R}^3$ such that $G$ is not uniformly positive definite, and there is no isometry $\p …
- 1,883