Smooth quasigroups and loops: forty-five years of incredible growth
The remarkable development of the theory of smooth quasigroups is surveyed.
The remarkable development of the theory of smooth quasigroups is surveyed.
In this paper, we explicitly determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles over the complex projective space for .
We define on an ordered semi simple symmetric space a family of spherical functions by an integral formula similar to the Harish-Chandra integral formula for spherical functions on a Riemannian symmetric space of non compact type. Associated with these spherical functions we define a spherical Laplace transform. This transform carries the composition product of invariant causal kernels onto the ordinary product. We invert this transform when is a complex group, a real form of , and when ...
, that is to say, Lorentzian manifolds with vanishing second derivative of the curvature tensor , are characterized by several geometric properties, and explicitly presented. Locally, they are a product where each factor is uniquely determined as follows: is a Riemannian symmetric space and is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., at some point), the curvature tensor turns out to...