Erlangen program at large: an overview
VV Kisil - Advances in applied analysis, 2012 - Springer
This is an overview of the Erlangen Program at Large. Study of objects and properties, which
are invariant under a group action, is very fruitful far beyond traditional geometry. In this …
are invariant under a group action, is very fruitful far beyond traditional geometry. In this …
[图书][B] Geometry of Mobius transformations: Elliptic, parabolic and hyperbolic actions of sl2 (r)(with dvd-rom)
VV Kisil - 2012 - books.google.com
This book is a unique exposition of rich and inspiring geometries associated with Möbius
transformations of the hypercomplex plane. The presentation is self-contained and based on …
transformations of the hypercomplex plane. The presentation is self-contained and based on …
Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2
The Kepler problem is a dynamical system that is well defined not only on the Euclidean
plane but also on the sphere and on the hyperbolic plane. First, the theory of central …
plane but also on the sphere and on the hyperbolic plane. First, the theory of central …
The quantum harmonic oscillator on the sphere and the hyperbolic plane
A nonlinear model of the quantum harmonic oscillator on two-dimensional space of constant
curvature is exactly solved. This model depends on a parameter λ that is related with the …
curvature is exactly solved. This model depends on a parameter λ that is related with the …
Induced representations and hypercomplex numbers
VV Kisil - Advances in applied Clifford algebras, 2013 - Springer
In the search for hypercomplex analytic functions on the halfplane, we review the
construction of induced representations of the group G=\rm SL _2 (R). Firstly we note that G …
construction of induced representations of the group G=\rm SL _2 (R). Firstly we note that G …
Conformal symmetries of spacetimes
FJ Herranz, M Santander - Journal of Physics A: Mathematical …, 2002 - iopscience.iop.org
In this paper, we give a unified and global new approach to the study of the conformal
structure of the three classical Riemannian spaces as well as of the six relativistic and non …
structure of the three classical Riemannian spaces as well as of the six relativistic and non …
Superintegrability on three-dimensional Riemannian and relativistic spaces of constant curvature
FJ Herranz, Á Ballesteros - SIGMA. Symmetry, Integrability and Geometry …, 2006 - emis.de
A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function,
which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the …
which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the …
[图书][B] Elements for physics: quantities, qualities, and intrinsic theories
A Tarantola - 2006 - Springer
Physics is very successful in describing the world: its predictions are often impressively
accurate. But to achieve this, physics limits terribly its scope. Excluding from its domain of …
accurate. But to achieve this, physics limits terribly its scope. Excluding from its domain of …
Maximal superintegrability on N-dimensional curved spaces
A unified algebraic construction of the classical Smorodinsky–Winternitz systems on the ND
sphere, Euclidean and hyperbolic spaces through the Lie groups SO (N+ 1), ISO (N) and SO …
sphere, Euclidean and hyperbolic spaces through the Lie groups SO (N+ 1), ISO (N) and SO …
The anisotropic oscillator on curved spaces: a new exactly solvable model
We present a new exactly solvable (classical and quantum) model that can be interpreted as
the generalization to the two-dimensional sphere and to the hyperbolic space of the two …
the generalization to the two-dimensional sphere and to the hyperbolic space of the two …