Displaying 301 – 320 of 575

Showing per page

Spherical functions on ordered symmetric spaces

Jacques Faraut, Joachim Hilgert, Gestur Ólafsson (1994)

Annales de l'institut Fourier

We define on an ordered semi simple symmetric space = G / H 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 G is a complex group, H a real form of G , and when ...

Split octonions and generic rank two distributions in dimension five

Katja Sagerschnig (2006)

Archivum Mathematicum

In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space G ˜ 2 / P , where P is one of the maximal parabolic subgroups of the exceptional Lie group G ˜ 2 . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.

Sprays and homogeneous connections on 𝐑 × 𝑇𝑀

Alexandr Vondra (1992)

Archivum Mathematicum

The homogeneity properties of two different families of geometric objects playing a crutial role in the non-autonomous first-order dynamics - semisprays and dynamical connections on R × T M - are studied. A natural correspondence between sprays and a special class of homogeneous connections is presented.

Currently displaying 301 – 320 of 575