Classification of cylindrically symmetric static space-times according to their proper homothetic vector fields.
We discuss which semisimple locally symmetric spaces admit an AHS-structure invariant under local symmetries. We classify them for all types of AHS-structures and determine possible equivalence classes of such AHS-structures.
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.
We consider a vector bundle and the principal bundle of frames of . Let be a principal connection on and let be a linear connection on . We classify all principal connections on naturally given by and .
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 , they are denoted as and given by explicit expressions.
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.