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Teoreticheskaya i Matematicheskaya Fizika, 2025, Volume 225, Number 1, Pages 159–176
DOI: https://doi.org/10.4213/tmf10985 (Mi tmf10985) 		 
Differential equations and their general solutions, as well as nonexistence theorems for six invariant classes of the vacuum constraint equations

S. E. Stepanovab, J. Mikešc

a Financial University under the Government of the Russian Federation, Moscow, Russia
b Russian Institute for Scientific and Technical Information of the~Russian Academy of Sciences, Moscow, Russia
c Department of Algebra and Geometry, Palacky University, Olomouc, Czech Republic
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DOI: https://doi.org/10.4213/tmf10985
Abstract: In this paper, we classify the vacuum constraint equations of General Relativity using the representation theory of classical groups. We also provide general solutions for the differential equations of each class and prove vanishing (nonexistence) theorems for these solutions using the Bochner technique, which is an important tool in Geometric Analysis.
Keywords: Riemannian manifold, pointwise orthogonal decomposition, general relativistic constraint equations.
Received: 18.03.2025
Revised: 01.04.2025
Published: 30.09.2025
English version:
Theoretical and Mathematical Physics, 2025, Volume 225, Issue 1, Pages 1830–1843
DOI: https://doi.org/10.1134/S0040577925100095
Document Type: Article
MSC: MSC 2010: 53A45; 53C20
Language: Russian
Citation: S. E. Stepanov, J. Mikeš, “Differential equations and their general solutions, as well as nonexistence theorems for six invariant classes of the vacuum constraint equations”, TMF, 225:1 (2025), 159–176; Theoret. and Math. Phys., 225:1 (2025), 1830–1843
Citation in format AMSBIB
\Bibitem{SteMik25}
\by S.~E.~Stepanov, J.~Mike{\v s}
\paper Differential equations and their general solutions, as well as nonexistence theorems for six invariant classes of the~vacuum constraint equations
\jour TMF
\yr 2025
\vol 225
\issue 1
\pages 159--176
\mathnet{http://mi.mathnet.ru/tmf10985}
\crossref{https://doi.org/10.4213/tmf10985}
\transl
\jour Theoret. and Math. Phys.
\yr 2025
\vol 225
\issue 1
\pages 1830--1843
\crossref{https://doi.org/10.1134/S0040577925100095}
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