69 citations · 90 across the 9 of their papers we have counts for
5 papers · 1 filter
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 …
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…
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…