2023/2024

13th of February 2024

Asahi Tsuchida (Shiga University)

Title: On flatness of sub-Riemannian manifold

27th of February 2024

Marcin Zubilewicz (Warsaw University of Technology)

Title: On flatness of bi-Lagrangian structures induced by tangents to a pair of Lagrangian curves

Abstract: A bi-Lagrangian structure is a quadruple (M,ω,F,G), where (M,ω) is a symplectic manifold and F, G are complementary foliations of M with Lagrangian leaves. In his paper from 1993, Tabachnikov gave several interesting examples of bi-Lagrangian structures, including a certain bi-Lagrangian structure on a standard 2n-dimensional symplectic space foliated by F and G into affine tangent spaces of two generic Lagrangian submanifolds L,K respectively. He encouraged his readers to consider the following interesting question: for which Lagrangian submanifold-germs L,K the corresponding bi-Lagrangian structure of the above kind is flat with respect to its canonical (bi-Lagrangian) connection? In this talk we give an answer to this question for n=1 and report on our progress regarding the general case. Joint work with W. Domitrz.