English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study those real $\mathcal{C}^\infty$ foliations in complex surfaces whoseleaves are holomorphic curves. The main motivation is to try and understandthese foliations in neighborhoods of curves: can we expect the space offoliations in a fixed neighborhood to be infinite-dimensional, or are theresome contexts under which every such foliation is holomorphic? We give somerestrictions and study in more details the geometry of foliations whose leavesbelong to a holomorphic family of holomorphic curves. In particular, weclassify all real-analytic foliations on neighborhoods of curves which arelocally diffeomorphic to foliations by lines, under some non-degeneracyhypothesis.

About $\mathcal{C}^\infty$ foliations by holomorphic curves on complex surfaces