Almost complex structures that model nonlinear geometries
Let X be a distribution on a \(C^{\infty}\)-manifold M and \(\omega\) be a non-degenerate 2-form on M. X is ``Lagrangian'' if \(X_ p\), \(p\in M\) is a maximally isotropic subspace of the tangent space at p relative to \(\omega_ p\). Under the assumption that the tangent bundle of M splits into two Lagrangian distributions X and Y, this paper studies the structure ((X,Y),g,\(\omega)\), where g is a metric on X. It deals with almost complex structures, Finsler geometry, general relativity and Cartan connections.
scientific article; zbMATH DE number 4044655
scientific article