On 𝑛-dimensional Lorentz manifolds admitting an isometry group of dimension 𝑛(𝑛-1)/2+1

Matsuda, Hiroo

doi:10.1090/S0002-9939-1987-0884474-1

On $n$-dimensional Lorentz manifolds admitting an isometry group of dimension $n(n-1)/2+1$
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Proc. Amer. Math. Soc. 100 (1987), 329-334 Request permission

Abstract:

We classify connected $n$-dimensional Lorentz manifolds admitting an isometry group of dimension $n(n - 1)/2 + 1$ with compact isotropy subgroup $(n \geq 5)$.

References

Shigeru Ishihara, Homogeneous Riemannian spaces of four dimensions, J. Math. Soc. Japan 7 (1955), 345–370. MR 82717, DOI 10.2969/jmsj/00740345
Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886, DOI 10.1007/978-3-642-61981-6
Hiroo Matsuda, A note on an isometric imbedding of upper half-space into the anti de Sitter space, Hokkaido Math. J. 13 (1984), no. 2, 123–132. MR 746520, DOI 10.14492/hokmj/1381757712
Katsumi Nomizu, The Lorentz-Poincaré metric on the upper half-space and its extension, Hokkaido Math. J. 11 (1982), no. 3, 253–261. MR 680814, DOI 10.14492/hokmj/1381757803
Morio Obata, On $n$-dimensional homogeneous spaces of Lie groups of dimension greater than $n(n-1)/2$, J. Math. Soc. Japan 7 (1955), 371–388. MR 82718, DOI 10.2969/jmsj/00740371
Barrett O’Neill, Semi-Riemannian geometry, Pure and Applied Mathematics, vol. 103, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity. MR 719023
Joseph A. Wolf, Spaces of constant curvature, 5th ed., Publish or Perish, Inc., Houston, TX, 1984. MR 928600
Kentaro Yano, On $n$-dimensional Riemannian spaces admitting a group of motions of order $n(n-1)/2+1$, Trans. Amer. Math. Soc. 74 (1953), 260–279. MR 52860, DOI 10.1090/S0002-9947-1953-0052860-X