GL(2)‐geometry and complex structures

We study G L ( 2 ) -structures on differential manifolds. A -structure is a smooth field of rational normal curves in the tangent bundle manifold. provide an explicit construction canonical connection for any dimension greater than 3. Moreover, we prove that even-dimensional manifold defines certain almost-complex structure over original Further, exploit to various notions integrability -structures. For this, develop twistor-like construction. In particular, 4 torsion-free if and only associated integrable.