Open Access
On conformally reducible pseudo-Riemannian spaces
Author(s) -
T. I. Shevchenko,
Тетяна Сергіївна Спічак,
Дмитро Миколайович Дойков
Publication year - 2021
Publication title -
trudy meždunarodnogo geometričeskogo centra/pracì mìžnarodnogo geometričnogo centru
Language(s) - English
Resource type - Journals
eISSN - 2409-8906
pISSN - 2072-9812
DOI - 10.15673/tmgc.v14i2.2097
Subject(s) - conformal map , mathematics , pure mathematics , conformal geometry , ideal (ethics) , mathematical analysis , algebra over a field , conformal field theory , epistemology , philosophy
The present paper studies the main type of conformal reducible conformally flat spaces.
We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping.
This allows to carry out the complete classification of these spaces.
The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity.
Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces.
Research is carried out locally in tensor shape.