Ellipsoidal billiards in pseudo-Euclidean spaces and relativistic quadrics
نویسندگان
چکیده
منابع مشابه
Spaces of pseudo-Riemannian geodesics and pseudo-Euclidean billiards
Many classical facts in Riemannian geometry have their pseudoRiemannian analogs. For instance, the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. We discuss the geometry of these structures in detail, as well as introduce an...
متن کاملSpaces of pseudo - Riemannian geodesics and pseudo - Euclidean billiards Boris
In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...
متن کاملIntegrable ellipsoidal billiards with separable potentials, billiards on quadrics, and the Poncelet theorem
One of the best known discrete integrable systems is the billiard inside an n-dimensional ellipsoid. Veselov showed that generic complex invariant manifolds of the algebraic billiard map are open subsets of (coverings of) hyperelliptic Jacobians and that the restriction of the map to such manifolds is described by the shift by a constant vector (an algebraic addition law). Later, Dragovic and R...
متن کاملPhone classification in pseudo-euclidean vector spaces
Recently we have proposed a structural framework for modelling speech, which is based on patterns of phonological distinctive features, a linguistically well-motivated alternative to standard vector-space acoustic models like HMMs. This framework gives considerable representational freedom by working with features that have explicit linguistic interpretation, but at the expense of the ability t...
متن کاملFrom the Lorentz Transformation Group in Pseudo-Euclidean Spaces to Bi-gyrogroups
The Lorentz transformation of order $(m=1,n)$, $ninNb$, is the well-known Lorentz transformation of special relativity theory. It is a transformation of time-space coordinates of the pseudo-Euclidean space $Rb^{m=1,n}$ of one time dimension and $n$ space dimensions ($n=3$ in physical applications). A Lorentz transformation without rotations is called a {it boost}. Commonly, the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2012
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.06.004