G. M. Kuz'mina, “Some generalizations of the Riemann spaces of Einstein”, Mat. Zametki, 16:4 (1974), 619–622; Math. Notes, 16:4 (1974), 961

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Matematicheskie Zametki, 1974, Volume 16, Issue 4, Pages 619–622 (Mi mzm7502)

This article is cited in 11 scientific papers (total in 11 papers)

Some generalizations of the Riemann spaces of Einstein

G. M. Kuz'mina

Moscow Engineering Physics Institute

Full-text PDF (289 kB) Citations (11)

Abstract: We introduce a class of Riemann structures, called generalized Einstein structures of index $2e$, of which Einstein spaces are a particular case. We show that these structures are stationary for functions introduced on a family of Riemann structures of the compact manifold of H. Weyl. This result solves a problem of M. Berger. As examples of structures which are generalized Einstein structures over all indices we cite homogeneous compact Riemann spaces with a nondecomposable isotropy group and products of such spaces.

Received: 25.05.1973

English version:
Mathematical Notes, 1974, Volume 16, Issue 4, Pages 961–963
DOI: https://doi.org/10.1007/BF01104264

Bibliographic databases:

UDC: 513

Language: Russian

Citation: G. M. Kuz'mina, “Some generalizations of the Riemann spaces of Einstein”, Mat. Zametki, 16:4 (1974), 619–622; Math. Notes, 16:4 (1974), 961–963

Citation in format AMSBIB

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\paper Some generalizations of the Riemann spaces of Einstein

\jour Mat. Zametki

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\pages 619--622

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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=372782}

\zmath{https://zbmath.org/?q=an:0309.53042}

\transl

\jour Math. Notes

\yr 1974

\vol 16

\issue 4

\pages 961--963

\crossref{https://doi.org/10.1007/BF01104264}

Linking options:

https://www.mathnet.ru/eng/mzm7502

https://www.mathnet.ru/eng/mzm/v16/i4/p619

This publication is cited in the following 11 articles:

Synthesis Lectures on Mathematics & Statistics, Aspects of Differential Geometry III, 2017
Peter B. GILKEY, JeongHyeong PARK, Kouei SEKIGAWA, “Universal curvature identities and Euler–Lagrange formulas for Kähler manifolds”, J. Math. Soc. Japan, 68:2 (2016)
JeongHyeong Park, “Euler–Lagrange formulas for pseudo-Kähler manifolds”, Journal of Geometry and Physics, 99 (2016), 239
Synthesis Lectures on Mathematics & Statistics, Aspects of Differential Geometry I, 2015
P. Gilkey, J.H. Park, “Analytic continuation, the Chern–Gauss–Bonnet theorem, and the Euler–Lagrange equations in Lovelock theory for indefinite signature metrics”, Journal of Geometry and Physics, 88 (2015), 88
Alberto Navarro, José Navarro, “Dimensional curvature identities on pseudo-Riemannian geometry”, Journal of Geometry and Physics, 86 (2014), 554
Y. Euh, P. Gilkey, J.H. Park, K. Sekigawa, “Transplanting geometrical structures”, Differential Geometry and its Applications, 31:3 (2013), 374
Jungchan Lee, Jeonghyeong Park, Kouei Sekigawa, “CURVATURE IDENTITIES DERIVED FROM AN INTEGRAL FORMULA FOR THE FIRST CHERN NUMBER”, Bulletin of the Korean Mathematical Society, 50:4 (2013), 1261
P. Gilkey, J.H. Park, K. Sekigawa, “Universal curvature identities II”, Journal of Geometry and Physics, 62:4 (2012), 814
Yunhee Euh, JeongHyeong Park, Kouei Sekigawa, “Critical metrics for quadratic functionals in the curvature on 4-dimensional manifolds”, Differential Geometry and its Applications, 29:5 (2011), 642
P. Gilkey, J.H. Park, K. Sekigawa, “Universal curvature identities”, Differential Geometry and its Applications, 29:6 (2011), 770

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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