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Results tagged with riemannian-geometry
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user 27069
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.
5
votes
Conformal vector field on the sphere
The group of conformal diffeomorphisms of the sphere $\mathbb{S}^d$ is isomorphic to SO(d+1,1) via the isomorphism
$$(\mathbb{H}^{d+1},\partial \mathbb{H}^{d+1}) \simeq (B^{d+1},\mathbb{S}^d)$$
where …
- 654
0
votes
twisted Poisson structures, degenerate metrics and integrability properties of (2,0)-tensors
i might have a partial answer, at least for the symmetric case. however my reasoning might not be completely stringent, so i still would like to read a better argument.
Let $X,Y\in \Gamma(Image(g^{\s …
- 654
9
votes
3
answers
475
views
twisted Poisson structures, degenerate metrics and integrability properties of (2,0)-tensors
Given a regular (constant rank) bi-vector $\Pi \in \Gamma(\bigwedge^2TM)$ on a smooth manifold $M$ the necessary and sufficient condition for the image of $\Pi^\sharp:T^*M\to TM$ to be an integrable d …
- 654