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Storm, Reinier. The Classification of 7- and 8-dimensional Naturally Reductive Spaces. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1246-1274. doi: 10.4153/S0008414X19000300
@article{10_4153_S0008414X19000300,
author = {Storm, Reinier},
title = {The {Classification} of 7- and 8-dimensional {Naturally} {Reductive} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {1246--1274},
year = {2020},
volume = {72},
number = {5},
doi = {10.4153/S0008414X19000300},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000300/}
}
TY - JOUR AU - Storm, Reinier TI - The Classification of 7- and 8-dimensional Naturally Reductive Spaces JO - Canadian journal of mathematics PY - 2020 SP - 1246 EP - 1274 VL - 72 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000300/ DO - 10.4153/S0008414X19000300 ID - 10_4153_S0008414X19000300 ER -
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[1] , , and , The classification of naturally reductive homogeneous spaces in dimensions n⩽6. Differential Geom. Appl. 39(2015), 59–92. https://doi.org/10.1016/j.difgeo.2014.11.005 Google Scholar | DOI
[2] , , and , Quaternionic Heisenberg groups as naturally reductive homogeneous spaces. Int. J. Geom. Methods Mod. Phys. 12(2015), 1560007, 10. https://doi.org/10.1142/S0219887815600075 Google Scholar
[3] and , On homogeneous Riemannian manifolds. Duke Math. J. 25(1958), 647–669. Google Scholar | DOI
[4] and , Representations of compact Lie groups. Graduate Texts in Mathematics, 98, Springer, New York, 1985. https://doi.org/10.1007/978-3-662-12918-0 Google Scholar | DOI
[5] , Sur une classe remarquable d’espaces de Riemann. Bull. Soc. Math. France 54(1926), 214–264. 10.24033/bsmf.1105 Google Scholar | DOI
[6] and , Naturally reductive metrics and Einstein metrics on compact Lie groups. Mem. Amer. Math. Soc. 18(1979), 215, iii + 72. Google Scholar
[7] , , , and , On nearly parallel G -structures. J. Geom. Phys. 23(1997), 259–286. https://doi.org/10.1016/S0393-0440(97)80004-6 Google Scholar | DOI
[8] , Naturally reductive homogeneous Riemannian manifolds. Canad. J. Math. 37(1985), 467–487. https://doi.org/10.4153/CJM-1985-028-2 Google Scholar | DOI
[9] , On the geometry of groups of Heisenberg type. Bull. London Math. Soc. 15(1983), 35–42. https://doi.org/10.1112/blms/15.1.35 Google Scholar | DOI
[10] , Diploma Thesis (in German): Einfach-zusammenhängende kompakte homogene Räume bis zur Dimension 9. 06 1988. https://doi.org/10.13140/2.1.4088.8324 Google Scholar | DOI
[11] , On differential geometry and homogeneous spaces. I, II. Proc. Natl Acad. Sci. USA 42(1956), 258–261, 354–357. Google Scholar | DOI
[12] , Counterexample to the “second Singer’s theorem”. Ann. Global Anal. Geom. 8(1990), 2, 211–214. https://doi.org/10.1007/BF00128004 Google Scholar | DOI
[13] and , Four-dimensional naturally reductive homogeneous spaces. Rend. Sem. Mat. Univ. Politec. Torino, (Special Issue): 223–232 (1984), 1983. Conference on differential geometry on homogeneous spaces (Turin, 1983). Google Scholar
[14] and , Classification of five-dimensional naturally reductive spaces. Math. Proc. Cambridge Philos. Soc. 97(1985), 3, 445–463. https://doi.org/10.1017/S0305004100063027 Google Scholar | DOI
[15] , Invariant affine connections on homogeneous spaces. Amer. J. Math. 76(1954), 33–65. Google Scholar | DOI
[16] , A new construction of naturally reductive spaces. Transform. Groups 23(2018), 2, 527–553. https://doi.org/10.1007/s00031-017-9446-5 Google Scholar | DOI
[17] , Structure theory of naturally reductive spaces. Differential Geom. Appl. 64(2019), 174–200. Google Scholar | DOI
[18] , Locally homogeneous Riemannian manifolds. Rend. Sem. Mat. Univ. Politec. Torino 50(1993), 4, 411–426. 1992. Differential geometry (Turin, 1992). Google Scholar
[19] and , Homogeneous structures on Riemannian manifolds. London Mathematical Society Lecture Note Series, 83, Cambridge University Press, Cambridge, 1983. https://doi.org/10.1017/CBO9781107325531 Google Scholar | DOI
[20] , Totally geodesic hypersurfaces of naturally reductive homogeneous spaces. Osaka J. Math. 33(1996), 3, 697–707. Google Scholar
[21] , The normal homogeneous space has positive sectional curvature. Proc. Amer. Math. Soc. 127(1999), 4, 1191–1194. https://doi.org/10.1090/S0002-9939-99-04613-4 Google Scholar | DOI
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