×

zbMATH — the first resource for mathematics

Geodesic multiplication and the theory of gravity. (English) Zbl 0806.53085
Summary: Nonassociative algebraic systems called local geodesic loops and their tangent Akivis algebras are considered. The construction of geo-odular structure of a manifold with an affine connection is briefly reviewed. A possible role of these algebraic structures in classical and quantum gravity is discussed.

MSC:
53Z05 Applications of differential geometry to physics
83E30 String and superstring theories in gravitational theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Sabinin L. V., Dokl. Akad. Nauk SSSR 233 pp 800– (1977)
[2] Sabinin L. V., Trans. Inst. Phys. Estonian Acad. Sci. 66 pp 24– (1990)
[3] Akivis M. A., Sibirski Mat. J. 19 pp 243– (1978) · Zbl 0409.53008 · doi:10.1007/BF00970497
[4] Kikkawa M., Hiroshima J. Univ. Ser. A-l. Math. 28 pp 199– (1964)
[5] DOI: 10.1090/S0002-9947-1943-0009962-7 · doi:10.1090/S0002-9947-1943-0009962-7
[6] Mal’tsev A., Mat. Sb. 36 pp 569– (1955)
[7] DOI: 10.4153/CJM-1965-056-8 · Zbl 0138.25601 · doi:10.4153/CJM-1965-056-8
[8] Akivis M. A., Sibirski Mat. J. 17 pp 5– (1976) · Zbl 0337.53018 · doi:10.1007/BF00969285
[9] DOI: 10.1007/BF00759173 · Zbl 0362.53013 · doi:10.1007/BF00759173
[10] Alexandrov A. N., Teor. Mat. Fiz. 38 pp 71– (1979)
[11] Kuusk P., Trans. Tallinn Techn. Univ. 733 pp 33– (1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.