{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T08:31:03Z","timestamp":1771662663083,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,5]],"date-time":"2022-06-05T00:00:00Z","timestamp":1654387200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Weyl and Finsler spaces. Geodesic line equations are constructed where coefficients can be divided into depending on the metric tensor (relating to the gravitational interaction) and depending on the vector field (relating to the electromagnetic interaction). If there is no gravity, the geodesics turn into the equations of charge motion in the electromagnetic field. Furthermore, symmetric six-dimensional electrodynamics can be reduced to traditional four-dimensional Maxwell system, where two additional time dimensions are compactified. A purely geometrical interpretation of the concept of electromagnetic field and point electric charge is proposed.<\/jats:p>","DOI":"10.3390\/sym14061163","type":"journal-article","created":{"date-parts":[[2022,6,5]],"date-time":"2022-06-05T10:47:11Z","timestamp":1654426031000},"page":"1163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Six-Dimensional Manifold with Symmetric Signature in a Unified Theory of Gravity and Electromagnetism"],"prefix":"10.3390","volume":"14","author":[{"given":"Nikolay","family":"Popov","sequence":"first","affiliation":[{"name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov Str., 44\/2, 119333 Moscow, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2005-9467","authenticated-orcid":false,"given":"Ivan","family":"Matveev","sequence":"additional","affiliation":[{"name":"Federal Research Center \u201cComputer Science and Control\u201d of the Russian Academy of Sciences, Vavilov Str., 44\/2, 119333 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Einstein, A. 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The Differential Geometry of Finsler Spaces, Springer.","DOI":"10.1007\/978-3-642-51610-8"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bogoslovsky, G.Y. (1992). Theory of Locally Anisotropic Space-Time, Moscow State University. (In Russian).","DOI":"10.1088\/0264-9381\/9\/2\/019"},{"key":"ref_16","unstructured":"Gerasko, G.I. (2009). Beginnings of Finsler Geometry for Physicist, TETRU. (In Russian)."},{"key":"ref_17","unstructured":"Popov, N.N. (2020). Space-time structure in the microcosm and its relation to the properties of elementary particles. arXiv."},{"key":"ref_18","unstructured":"Pauli, W. (1981). Theory of Relativity, Dover Publications. New Edition."},{"key":"ref_19","unstructured":"Bogolyubov, N.N., and Shirkov, D.V. (1976). Introduction to a Theory of Quantized Fields, Nauka. (In Russian)."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/6\/1163\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:24:42Z","timestamp":1760138682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/6\/1163"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,5]]},"references-count":19,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["sym14061163"],"URL":"https:\/\/doi.org\/10.3390\/sym14061163","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,5]]}}}