In the present article the geometry of semi-Riemannian manifolds with nonholo-nomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where theâ€¦ (More)

We consider examples of the H-type groups with the natural horizontal distribution generated by the commutation relations of the group. In the contrast with the previous studies we furnish theâ€¦ (More)

We consider coefficient bodies Mn for univalent functions. Based on the LÃ¶wner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals areâ€¦ (More)

The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory. Inâ€¦ (More)

In the present paper we define quasimeromorphic mappings on homogeneous groups and study their properties. We prove an analogue of results of L. Ahlfors, R. Nevanlinna and S. Rickman, concerning theâ€¦ (More)

Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. Sub-Riemannian Geometry enjoys major differences from the Riemannianâ€¦ (More)

The present article applies the method of Geometric Analysis to the study H-type groups satisfying the J condition and finishes the series of works describing the Heisenberg group and the quaternionâ€¦ (More)

We construct examples of 2-step Carnot groups related to quaternions and study their fine structure and geometric properties. This involves the Hamiltonian formalism, which is used to obtain explicitâ€¦ (More)

The unit sphere S can be identified with the unitary group SU(2). Under this identification the unit sphere can be considered as a non-commutative Lie group. The commutation relations for the vectorâ€¦ (More)