Distributions, First Integrals and Legendrian Foliations

Maycol Falla Luza, Rudy Rosas

Producción científica: Contribución a una revistaArtículorevisión exhaustiva


We study germs of holomorphic distributions with “separated variables”. In codimension one, a well know example of this kind of distribution is given by dz=(y1dx1-x1dy1)+⋯+(ymdxm-xmdym),which defines the canonical contact structure on CP2m+1. Another example is the Darboux distribution dz=x1dy1+⋯+xmdym,which gives the normal local form of any contact structure. Given a germ D of holomorphic distribution with separated variables in (Cn, 0) , we show that there exists , for some κ∈ Z≥ 0 related to the Taylor coefficients of D, a holomorphic submersion HD:(Cn,0)→(Cκ,0)such that D is completely non-integrable on each level of HD. Furthermore, we show that there exists a holomorphic vector field Z tangent to D, such that each level of HD contains a leaf of Z that is somewhere dense in the level. In particular, the field of meromorphic first integrals of Z and that of D are the same. Between several other results, we show that the canonical contact structure on CP2m+1 supports a Legendrian holomorphic foliation whose generic leaves are dense in CP2m+1. So we obtain examples of injectively immersed Legendrian holomorphic open manifolds that are everywhere dense.

Idioma originalInglés
Páginas (desde-hasta)1157-1229
Número de páginas73
PublicaciónBulletin of the Brazilian Mathematical Society
EstadoPublicada - dic. 2022
Publicado de forma externa


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