منابع مشابه
Transitions: Contractions and Analytical Continuations of the Cayley-Klein Groups
As a foundation for Klein’s fundamental idea about the connection of geometry and its motion group and the unified description of all Cayley-Klein geometries, a method of group transitions including contractions as well as analytical continuations of the groups is developed. The generators and Casimir operators of an arbitrary Cayley-Klein group are obtained from those of the classical orthogon...
متن کاملMultiple Cayley-Klein metric learning
As a specific kind of non-Euclidean metric lies in projective space, Cayley-Klein metric has been recently introduced in metric learning to deal with the complex data distributions in computer vision tasks. In this paper, we extend the original Cayley-Klein metric to the multiple Cayley-Klein metric, which is defined as a linear combination of several Cayley-Klein metrics. Since Cayley-Klein is...
متن کاملNon-euclidean geometries: the Cayley-Klein approach
A. Cayley and F. Klein discovered in the nineteenth century that euclidean and non-euclidean geometries can be considered as mathematical structures living inside projective-metric spaces. They outlined this idea with respect to the real projective plane and established (“begründeten”) in this way the hyperbolic and elliptic geometry. The generalization of this approach to projective spaces ove...
متن کاملHomogeneous phase spaces: the Cayley–Klein framework
The metric structure of homogeneous spaces of rank-one and rank-two associated to the real pseudo-orthogonal groups SO(p, q) and some of their contractions (e.g., ISO(p, q), Newton–Hooke type groups. . . ) is studied. All these spaces are described from a unified setting following a Cayley–Klein scheme allowing to simultaneously study the main features of their Riemannian, pesudoRiemannian and ...
متن کاملTheta functions on covers of symplectic groups
We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. This representation is obtained from the residues of Eisenstein series on this group. If $r$ is odd, $nle r
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ژورنال
عنوان ژورنال: International Journal of Modern Physics A
سال: 1997
ISSN: 0217-751X,1793-656X
DOI: 10.1142/s0217751x97000244