arXiv subjects
Publications and source records attributed to Dmitry A. Kalinin.
The goal of the present paper is to investigate four dimensional Kahler manifolds admitting H-projective mappings with special attention to Einstein-Kahler manifolds of this type which can be interpreted as field configurations of the gravitational instantons.
The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in momenta. In the last part of the paper the quantum mechanics of scalar particle in curved space-time is studied with the use of proposed approach.
The paper is devoted to the investigation of four-dimensional Kahler manifolds admitting non-affine H-projective mappings. We find all such manifolds which are non-Einstein. In the paper also Kahler manifolds admitting infinitesimal H-projective transformations are determined. It is proved that the class of Kahler manifolds admitting H-projective mappings includes generalized equidistant Kahler manifolds. The explicit expression for the metrics of Ricci-flat four-dimensional generalized equidistant manifolds is given.