69 citations · 90 across the 9 of their papers we have counts for
10 papers
The rolling tangent space, a forgotten vision on parallel transport and geodesics
Constant Pinteaux, Gijs M. Tuynman
Given a submanifold , a curve and tangent vectors along , we roll the tangent space along . In doing so, we get an imprint/trace of …
The Super Orbit Challenge
Gijs M. Tuynman
When using the generally adopted definition of a super unitary representation, there are lots of super Lie groups for which the regular representation is not super unitary. I propo…
Super unitary representations revisited
Gijs M. Tuynman
With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular represe…
The metaplectic correction in geometric quantization
Gijs M. Tuynman
Let be a polarization on a symplectic manifold for which there exists a metalinear frame bundle. We show that for any other compatible polarization there exists a unique m…
Areas of spherical and hyperbolic triangles in terms of their midpoints
Gijs M. Tuynman
Let be either the 2-sphere $\SS^2 \subset\RR^3$ or the hyperbolic plane $\HH^2 \subset \RR^3$. If is a geodesic triangle on with corners at , we denote…
Integrating infinitesimal (super) actions
Gijs M. Tuynman
In this paper we generalize some results of Richard Palais to the case of Lie supergroups and Lie superalgebras. More precisely, let be a Lie supergroup, its Lie…
Geodesics on a supermanifold and projective equivalence of super connections
Thomas Leuther, Fabian Radoux, Gijs Tuynman
We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in…
Geometric Quantization of Superorbits: a Case Study
Gijs M. Tuynman
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geom…
Super Symplectic Geometry and Prequantization
Gijs M. Tuynman
We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non ho…
Obstruction Results in Quantization Theory
Mark J. Gotay, Hendrik B. Grundling, Gijs M. Tuynman
We define the quantization structures for Poisson algebras necessary to generalise Groenewold and Van Hove's result that there is no consistent quantization for the Poisson algebra…