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Some remarks on Lie flows.

Miquel Llabrés, Agustí Reventós (1989)

Publicacions Matemàtiques

The first part of this paper is concerned with geometrical and cohomological properties of Lie flows on compact manifolds. Relations between these properties and the Euler class of the flow are given.The second part deals with 3-codimensional Lie flows. Using the classification of 3-dimensional Lie algebras we give cohomological obstructions for a compact manifold admits a Lie flow transversely modeled on a given Lie algebra.

Split octonions and generic rank two distributions in dimension five

Katja Sagerschnig (2006)

Archivum Mathematicum

In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space G ˜ 2 / P , where P is one of the maximal parabolic subgroups of the exceptional Lie group G ˜ 2 . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.

Stability of certain Engel-like distributions

Aritra Bhowmick (2021)

Czechoslovak Mathematical Journal

We introduce a higher dimensional analogue of the Engel structure, motivated by the Cartan prolongation of contact manifolds. We study the stability of such structure, generalizing the Gray-type stability results for Engel manifolds. We also derive local normal forms defining such a distribution.

Stability of Tangential Locally Conformal Symplectic Forms

Cristian Ida (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we firstly define a tangential Lichnerowicz cohomology on foliated manifolds. Next, we define tangential locally conformal symplectic forms on a foliated manifold and we formulate and prove some results concerning their stability.

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