Related papers: Extrinsic symplectic symmetric spaces
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
We study integral geometric properties of non-compact harmonic spaces.
We give an intrinsic characterization of multisymplectic manifolds that have the linear type of density-valued symplectic forms in each tangent space, prove Darboux-type theorems for these forms, and investigate their symmetries.
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…
We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.
We develop an electromagnetic symplectic structure on the space-time manifold by defining a Poisson bracket in terms of an invertible electromagnetic tensor F_{\mu\nu}. Moreover, we define electromagnetic symplectic diffeomorphisms by…
We define a symplectic structure on the space of non parametrized loops in $G_2$ manifold. We also develop some basics of intersection theory of Lagrangian submanifolds.
The complex projective spaces, considered as prequantized symplectic manifolds, are roughly to the complete symmetric functions as those projective spaces, regarded as complex-oriented manifolds, are to Newton's power sums.
The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of…
The objective of the current paper is essentially twofold. Firstly, to make clear the difference between two notions of rolling a Riemannian manifold over another, using a language accessible to a wider audience, in particular to readers…
We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…
We define 2-calibrated structures, which are analogs of symplectic structures in odd dimensions. We show the existence of differential topological constructions compatible with the structure.
We investigate the uniqueness of so-called exotic structures on certain exact symplectic manifolds by looking at how their symplectic properties change under small nonexact deformations of the symplectic form. This allows us to distinguish…
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…
We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique…
On a complex manifold $(M,J)$, we interpret complex symplectic and pseudo-K\"ahler structures as symplectic forms with respect to which $J$ is, respectively, symmetric and skew-symmetric. We classify complex symplectic structures on…
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show…
We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a…