140 research outputs found
Invariants and submanifolds in almost complex geometry
In this paper we describe the algebra of differential invariants for
GL(n,C)-structures. This leads to classification of almost complex structures
of general positions. The invariants are applied to the existence problem of
higher-dimensional pseudoholomorphic submanifolds
Nijenhuis tensors in pseudoholomorphic curves neighborhoods
Normal forms of almost complex structures in a neighborhood of
pseudoholomorphic curve are considered. We define normal bundles of such curves
and study the properties of linear bundle almost complex structures. We
describe 1-jet of the almost complex structure along a curve in terms of its
Nijenhuis tensor. For pseudoholomorphic tori we investigate the problem of
pseudoholomorphic foliation of the neighborhood. We obtain some results on
nonexistence of the tori deformation.Comment: 27 page
Examples of integrable sub-Riemannian geodesic flows
Motivated by a paper of Bolsinov and Taimanov DG/9911193 we consider
non-holonomic situation and exhibit examples of sub-Riemannian metrics with
integrable geodesic flows and positive topological entropy. Moreover the
Riemannian examples are obtained as "holonomization" of sub-Riemannian ones. A
feature of non-holonomic situation is non-compactness of the phase space.
We also exhibit a Liouvulle-integrable Hamiltonian system with topological
entropy of all integrals positive.Comment: 21 pages; Answer to the self-posed question is added: Is it possible
to construct Liouville-integrable Hamiltonian system with positive
topological entropies of all integrals? Yes and we present an exampl
- …