Geometry of third order ODE systems

Alexandr Medvedev

Displaying similar documents to “Geometry of third order ODE systems”

On the cohomology of vector fields on parallelizable manifolds

Yuly Billig, Karl-Hermann Neeb (2008)

Annales de l’institut Fourier

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In the present paper we determine for each parallelizable smooth compact manifold $M$ the second cohomology spaces of the Lie algebra $𝒱_{M}$ of smooth vector fields on $M$ with values in the module $\bar{Ω}_{M}^{p} = Ω_{M}^{p} / d Ω_{M}^{p - 1}$ . The case of $p = 1$ is of particular interest since the gauge algebra of functions on $M$ with values in a finite-dimensional simple Lie algebra has the universal central extension with center ${\bar{Ω}}_{M}^{1}$ , generalizing affine Kac-Moody algebras. The second cohomology $H^{2} (𝒱_{M}, {\bar{Ω}}_{M}^{1})$ classifies twists of the semidirect product...

Lefschetz coincidence numbers of solvmanifolds with Mostow conditions

Hisashi Kasuya (2014)

Archivum Mathematicum

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For any two continuous maps $f$ , $g$ between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of $f$ , $g$ . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.