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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

2 votes
0 answers
122 views

Are affine maps (wrt to a connection), which preserve a tensor field, given by a PDE?

Let $(M, \nabla)$ be a manifold together with a connection on $TM$ and let $T$ be a tensor field on $M$. Suppose the pseudogroup $\Gamma$ of locally defined smooth maps, that simultanously preserve th …
0 votes
0 answers
90 views

Do the germs of local vector fields which are generated by a Lie pseudogroup form a Lie alge...

Let $(M,g)$ a semi-Riemannian manifold, and let $\mathcal{G}$ a be Lie pseudogroup which acts by local isometries on $(M,g)$. Clearly the germs of all local killing vector fields at $p \in M$ form a L …