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Results tagged with riemannian-geometry
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user 542481
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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Comparison between riemannian distance of a manifold embedded in $\mathbf R^N$ and euclidean...
Let $M$ be a closed Riemannian manifold isometrically embedded in some $\mathbf R^N$, and moreover let $d_M$ be the Riemannian distance on $M$. It is clear that for $x,y \in M$ :
$$
|x-y| \leq d_M(x,y …
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Regularity of the eigenfunctions associated to perturbed laplacian on a compact manifold
Let $M$ be a closed manifold, I consider first order laplacian perturbation associated to a density $\rho \in \mathcal{C}^\infty(M)$ with $\rho > 0$ of the form :
$$
\Delta_{\rho} f = \Delta f + \lang …