Related papers: Twisted Legendre transformation
For two generalized Frobenius manifolds related by a Legendre-type transformation, we show that the associated integrable hierarchies of hydrodynamic type, which are called the Legendre-extended Principal Hierarchies, are related by a…
This article generalizes the theory of shifted symplectic structures to the relative context and non-geometric stacks. We describe basic constructions that naturally appear in this theory: shifted cotangent bundles and the AKSZ procedure.…
A theory of cotetrad fields on a four-dimensional manifold is considered. Its configuration space coincides with that of the Teleparallel Equivalent of General Relativity but its dynamics is much simpler. We carry out the Legendre…
In the generalized Legendre transform construction the Kaehler potential is related to a particular function. Here, the form of this function appropriate to the monopole metric is calculated from the known twistor theory of monopoles.
Embedded Lagrangian cobordisms between Legendrian submanifolds are produced from isotopy, spinning, and handle attachment constructions that employ the technique of generating families. Moreover, any Legendrian with a generating family has…
We are proposing Tulczyjew's triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These…
It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop…
The notion of twisted sectors play a crucial role in orbifold Gromov-Witten theory. We introduce the notion of dihedral twisted sectors in order to construct Lagrangian Floer theory on symplectic orbifolds and discuss related issues.
The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials. We show how the use of the well known integral…
This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).
The Witten-Dijkgraaf-Verlinde-Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class - the so-called Legendre transformations - were introduced by Dubrovin.…
In this paper we extend the well-know normal form theorem for Lagrangian submanifolds proved by A. Weinstein in symplectic geometry to the setting of k-symplectic manifolds.
We generalize the hyperkaehler quotient construction to the situation where there is no group action preserving the hyperkaehler structure but for each complex structure there is an action of a complex group preserving the corresponding…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an application, we describe hamiltonian flows as…
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…
In this article, we generalize the theory of discrete Lagrangian mechanics and variational integrators in two principal directions. First, we show that Lagrangian submanifolds of symplectic groupoids give rise to discrete dynamical systems,…
We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie…
Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven…
The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function…