20 questions linked to/from Finding a 1-form adapted to a smooth flow
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### Counterexample showing that G-invariant de Rham cohomology different from cohomology of G-invariant sub-complex?

If $G$ is a discrete or a Lie Group acting smoothly on a manifold $M$, we can define the algebra of $G$-invariant de Rham classes, $H(M)^G$, and we can also consider the cohomology of the sub-complex ...
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### A non integrable distribution which is totally geodesic

Is there a non integrable $2$ dimensional distribution $D$ of a $3$ dimensional Riemannian manifold such that the distribution is totally geodesic in the following sense: Every geodesic whose ...
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### Computer algebra for calculating curvature when the tensor metric is very big

Is there a computer algebra method to compute the curvature of a Riemannian metric on the plane when the metric tensor has long entries $E,F,G$ The computation by hand is very ...
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### Limit cycles as closed geodesics (in negatively or positively curved space)

EDIT: Here is a related post which concern quadratic vector fields rather than Van der Pol equation. In this linked post we see that the convexity of limit cycle play a crucial role. On ...
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### The adjoint operators as elliptic operators

Edit: It seems that the link "https://cms.math.ca/Events/Toulouse2004/abs/ss7.html#lt" which contains a talk by Loic Teyssier about homological equations and vanishing cycles is temporally ...
### Is there a connection $\nabla$ for which this particular non geodesible vector field $X$ satisfy $\nabla_X X=0$?
Let $X$ be the following vector field on $\mathbb{R}^2\setminus \{0\}$ \begin{align} x' &= x\,(1-x^2-y^2)(x^2+y^2-3) - y\,(2-x^2-y^2)\\ y' &= y\,(1-x^2-y^2)(x^2+y^2-3) + x\,(2-x^2-y^2). \...