CR-structures of codimension 2 on tangent bundles in Riemann-Finsler geometry

Abstract

We determine a 2-codimensional CR-structure on the slit tangent bundle $T_{0}M$ of a Finsler manifold $(M,F)$ by imposing a condition regarding the almost complex structure $\Psi$ associated to $F$ when restricted to the structural distribution of a framed $f$-structure. This condition is satisfied when $(M,F)$ is of scalar flag curvature (particularly flat) and in the Riemannian case $(M,g)$ this last condition means that $g$ is of constant curvature. This CR-structure is finally generalized by using one positive number but under more difficult conditions.

10 pages

References in corpus (1)

• The equivalence and the embedding problems for CR-structures of any codimension