Displaying similar documents to “On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation”

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

Archivum Mathematicum

Similarity:

Consider a flat symplectic manifold ( M 2 l , ω ) , l ≥ 2 , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If λ is an eigenvalue of the symplectic Dirac operator such that - ı l λ is not a symplectic Killing number, then l - 1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.

Symplectic Killing spinors

Svatopluk Krýsl (2012)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let ( M , ω ) be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection ∇ . Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one...

Symplectic twistor operator and its solution space on ℝ 2

Marie Dostálová, Petr Somberg (2013)

Archivum Mathematicum

Similarity:

We introduce the symplectic twistor operator T s in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on ℝ 2 .

Symplectic embedding of thin discs into a ball

Takeo Nishinou (2004)

Mathematica Bohemica

Similarity:

We perform symplectic embeddings of ‘thin’ discs into a small ball in arbitrary dimension, using the symplectic folding construction.

Invariant properties of the generalized canonical mappings

Stanisław Janeczko (1999)

Banach Center Publications

Similarity:

One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.