29 Jan 2003

Boris Kruglikov "Geometry of Tangent and Normal bundles - II".

This time I will define two canonical almost complex structures on the total space of the normal bundle to a pseudoholomorphic submanifold. One is surprisingly close to a complex one and the other bears more features of the 1-jet of the almost complex structure along a submanifold. I will describe the exact relation between them.

After this I will relate these structures to the two problems. One was posed by V.Arnold in relation to his Floquet-type theory of elliptic curves neighborhoods. Another appears in the J.Moser's paper in Inventiones (1995) and concerns the normal form of the linearization of the double-periodic Cauchy-Riemann equation.

I will also briefly mention the possible parallels in other geometries. In the beginning of the talk I will briefly recall from the 1st lecture the main ingredients important to follow the material.