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Igor Zelenko
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Igor Zelenko Department of Mathematics Texas A&M Univerisity College Station, TX 77843-3368, USA; tel: +1-979-845-5837 fax: +1-979-845-6028 e-mail: zelenko@math.tamu.edu |
The main direction of my research is the construction of the curvature-type differential invariants for a wide class of geometric structures on manifolds with applications to
a) state-feedback equivalence of control systems;
b) equivalence of nonholonomic vector distributions, fields of cones, ordinary and partial differential equations;
c) optimality properties of extremals of optimal control problems;
d) qualitative study of Hamiltonian systems.
The approach is based on the study of differential geometry of curves in Grassmannians, Lagrange Grassmannians, and spaces of flags.
Among other topics of my research are
1) geodesic (projective) equivalence of sub-Riemannian metrics ;
2) invariant description of flat control systems;
3) sub-Riemannian Laplace-Beltrami operator.