Search Results

Let $M$ be a compact Riemannian manifold. The norm of vector fields are computed with respect to the metric. Moreover for every distribution $D$, the orthogonal projection on $D$ is den …

Motivation: The aim of this post is to extend the Lie algebra of a foliation to a bigger Lie algebra. We assume that a manifold $M$ is foliated by compat leaves. The Lie algebra of the foliation is th …

No. 706, Séminaire Bourbaki, Vol. 1988/89, 155–181 That is, two topologically equivalent foliations have the same Godbillon-Vey class. What are some updates on this conjecture? …

Inspired by An algebraic Hamiltonian vector field with a finite number of periodic orbits (2) we ask if there is a 1 dimensional analytic foliation of $\mathbb{R}^4$ which has at least 1 compact l …

Can the Reeb foliation of $S^3$ be realized as foliation associated to stable(or unstable) manifolds of a hyperbolic discrete dynamic on $S^3$?If yes what is a precise formulation for that Hyp …

What is an example of a non vanishing smooth vector field on a manifold $M$ whose corresponding foliation is a Riemannian foliation with respect to no Riemannian metric on $M$

Inspired by this question about Jacobi equation. conjugate points and limit cycle theory we ask the following question: Is there a geodesible 1 dimensional foliation $\mathcal{F}$ on a manifold $M$, …

Inspired by this question on homothety vector fields we realize that non homotheticity is some how an intrinsic property of the foliation associated to the vector field. See the comment by Prof. Bryan …

This note contains an affirmative answer to the question https://maco.lu.ac.ir/article-1-86-en.html

Note: In this question we do not specify the dimension of the foliations under consideration but we require that the foliation has non trivial dimension. …

Is there a polynomial vector field on $\mathbb{R}^2$ whose corresponding singular complex foliation of $\mathbb{C}^2 $ admits a complex limit cycle $L$ such that $L$ does not intersect the real pl …

Is there a polynomial vector field $X$ on $\mathbb{R}^2$ such that every complex limit cycle of the corresponding foliation of $\mathbb{C}^2$ must necessarily intersect the real plane $\mathbb{R}^2$. …

What is an example of a Lie group $G$ with two codimension one foliations $F_1 $ and $F_2$ such that they generate two different Godbilon–Vey invariants in $H^3(G)$? …

**I have already asked this question on MSE https://math.stackexchange.com/questions/4272279/1-dimensional-foliation-of-surfaces-with-prescribed-graph-of-foliation ** Definition of the graph of a fo …

The reason of geodesibility of case $1$ and three matrices in case $2$ is discussed in the following post which is essentially based on page 71 of "Geometry of foliations" by Philippe Tondeur, Proposition …