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Classification of Monge-Ampère equations with two variables

Boris Kruglikov (1999)

Banach Center Publications

This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.

Classification of principal connections naturally induced on W 2 P E

Jan Vondra (2008)

Archivum Mathematicum

We consider a vector bundle E → M and the principal bundle P E of frames of E . Let K be a principal connection on P E and let Λ be a linear connection on M . We classify all principal connections on W 2 P E = P 2 M × M J 2 P E naturally given by K and Λ .

Classification of projective space motions with only plane trajectories

Adolf Karger (1989)

Aplikace matematiky

The paper contains the solution of the classification problem for all motions in the complex projective space, which have only plane trajectories. It is shown that each such motion is a submanifold of a maximal motion with the same property. Maximal projective space motions with only plane trajectories are determined by special linear submanifolds of dimensions 2, 3, 5, 8 in G L ( 4 , C ) , they are denoted as R , E 1 , . . . , E 6 , S 1 , S 2 and given by explicit expressions.

Classifications of star products and deformations of Poisson brackets

Philippe Bonneau (2000)

Banach Center Publications

On the algebra of functions on a symplectic manifold we consider the pointwise product and the Poisson bracket; after a brief review of the classifications of the deformations of these structures, we give explicit formulas relating a star product to its classifying formal Poisson bivector.

Clifford algebra with Reduce

Brackx, Freddy, Constales, Denis, Delanghe, Richard, Serras, Herman (1987)

Proceedings of the Winter School "Geometry and Physics"

Clifford algebras, Möbius transformations, Vahlen matrices, and B -loops

Jimmie Lawson (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we show that well-known relationships connecting the Clifford algebra on negative euclidean space, Vahlen matrices, and Möbius transformations extend to connections with the Möbius loop or gyrogroup on the open unit ball B in n -dimensional euclidean space ℝ n . One notable achievement is a compact, convenient formula for the Möbius loop operation a * b = ( a + b ) ( 1 - a b ) - 1 , where the operations on the right are those arising from the Clifford algebra (a formula comparable to ( w + z ) ( 1 + w ¯ z ) - 1 for the Möbius loop multiplication...

Clifford and harmonic analysis on cylinders and torii.

Rolf Sören Krausshar, John Ryan (2005)

Revista Matemática Iberoamericana

Cotangent type functions in Rn are used to construct Cauchy kernels and Green kernels on the conformally flat manifolds Rn/Zk where 1 < = k ≤ M. Basic properties of these kernels are discussed including introducing a Cauchy formula, Green's formula, Cauchy transform, Poisson kernel, Szegö kernel and Bergman kernel for certain types of domains. Singular Cauchy integrals are also introduced as are associated Plemelj projection operators. These in turn are used to study Hardy spaces in this...

Clifford approach to metric manifolds

Chisholm, J. S. R., Farwell, R. S. (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis { e j : j = 1 , ⋯ , n } satisfying the condition { e i , e j } ≡ e i e j = e j e i = 2 I η i j , where I denotes the unit scalar of the algebra and ( η i j ) the nonsingular Minkowski...

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