sigma10-090. 234KB Jun 04 2011 12:10:45 AM
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In 1919–1920 Cartan has shown in [ 4 ] (using mostly projective arguments and his exterior differential systems in involution and exteriorly orthogonal forms tools) that space forms
Finally, we note that properties of horizontal Chern forms in relation with basic properties of classical Chern forms must be studied, as well as the independence of these forms
In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a St¨ackel transformed version on the 2-sheet hyperboloid are
There is an argument that the action of this twisted diffeomorphism can be regarded as a remnant of the classical diffeomorphism, where the change of the background
We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been
Key words: quiver variety; quiver variety with multiplicities; non-symmetric Kac–Moody algebra; Painlev´e equation; meromorphic connection; reflection functor; middle convolution..
Under such settings, moreover, it is obvious that one should choose a value of E (consequently ζ 2 and ζ 1 would be determined for specific values of the ordering ambiguity
The invertible transformations allow us to obtain objects associated with integrability of equations ( 1.13 ), ( 1.17 ) (such as conservation laws and higher symmetries) from
