Reduction of Jacobi Manifolds via Dirac Structures Theory
نویسندگان
چکیده
We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the generalized Lie bialgebroid of a Jacobi manifold (M,Λ, E) for which 1 is an admissible function and Jacobi quotient manifolds of M . We study Jacobi reductions from the point of view of Dirac structures theory and we present some examples and applications.
منابع مشابه
Dirac Structures and Generalized Complex Structures on TM × R h by Izu Vaisman
We consider Courant and Courant-Jacobi brackets on the stable tangent bundle TM ×R of a differentiable manifold and corresponding Dirac, Dirac-Jacobi and generalized complex structures. We prove that Dirac and Dirac-Jacobi structures on TM × R can be prolonged to TM × R, k > h, by means of commuting infinitesimal automorphisms. Some of the stable, generalized, complex structures are a natural g...
متن کاملE1(M )-Dirac structures and Jacobi structures
Using E1(M)-Dirac structures, a notion introduced by A. Wade, we obtain conditions under which a submanifold of a Jacobi manifold has an induced Jacobi structure, generalizing the result obtained by Courant for Dirac structures and submanifolds of a Poisson manifold.
متن کاملRemarks on Contact and Jacobi Geometry
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of ...
متن کامل9 S ep 2 00 8 Dirac and Nonholonomic Reduction
Several aspects of Dirac reduction are compared and formulated from the same geometric point of view. A link with nonholonomic reduction is found. The theory of optimal momentum maps and reduction is extended from the category of Poisson manifolds to that of closed Dirac manifolds. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in det...
متن کاملHaantjes Structures for the Jacobi–Calogero Model and the Benenti Systems
In the context of the theory of symplectic-Haantjes manifolds, we construct the Haantjes structures of generalized Stäckel systems and, as a particular case, of the quasi-biHamiltonian systems. As an application, we recover the Haantjes manifolds for the rational Calogero model with three particles and for the Benenti systems.
متن کامل