Conformal mappings of Riemannian manifolds preserving the generalized Einstein tensor
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Date
2018
Journal Title
Journal ISSN
Volume Title
Publisher
Slovak University of Technology in Bratislava
Abstract
We study conformal mappings preserving the generalized Einstein tensor. We have derived corresponding partial differential equations and their integrability conditions. In addition to the generalized Einstein tensor we got other invariants of the mappings. Also we have proved that orientable compact manifolds equipped by positive definite metric, do not admit conformal mappings preserving the generalized Einstein tensor.
Description
Keywords
affine connection, Riemannian manifolds, conformal mappings, generalized Einstein tensor
Citation
CHEREVKO Yevhen, BEREZOVSKI Vladimir, CHEPURNA Olena. Conformal mappings of Riemannian manifolds preserving the generalized Einstein tensor. 17 Conference on Applied Mathematics APLIMAT 2018. Proceedings. P. 224-231