Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T23:30:09.156Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Homogeneous Einstein Manifolds

Published online by Cambridge University Press:  22 January 2016

Arthur A. Sagle
Arthur A. Sagle*
Affiliation:
University of Minnesota
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a connected Lie group and H a closed subgroup with Lie algebra such that in the Lie algebra g of G there exists a subspace m with (subspace direct sum) and In this case the corresponding manifold M = G/H is called a reductive homogeneous space and (g,) (or (G,H)) a reductive pair. In this paper we shall show how to construct invariant pseudo-Riemannian connections on suitable reductive homogeneous spaces M which make M into an Einstein manifold.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 39 , August 1970 , pp. 81 - 106
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Husemoller, D., Fiber Bundles. McGraw-Hill Company, 1967.Google Scholar
[2] Jacobson, N., Lie Algebras, John Wiley, 1962.Google Scholar
[3] Kostant, B., On holonomy and homogeneous spaces, Nagoya Math. Jol. vol. 12 (1957), 31–54.Google Scholar
[4] Loos, O., Symmetric Spaces, W.A. Benjamin, to appear.Google Scholar
[5] Nomizu, K., Invariant affine connections on homogeneous spaces, Amer. Math. Jol., vol. 76 (1954), 33–65.Google Scholar
[6] Sagle, A., A note on simple anti-commutative algebras obtained from reductive homogeneous spaces, Nagoya Math. Jol., vol. 31 (1968), 105–124.CrossRefGoogle Scholar
[7] Sagle, A., On anti-commutative algebras and homogeneous spaces, Jol. Math, and Mech., vol. 16 (1967), 1381–1393.Google Scholar
[8] Sagle, A., On homogeneous spaces, holonomy and nonassociative algebras, Nagoya Math. Jol., vol. 32 (1968), 373–394.CrossRefGoogle Scholar
[9] Sagle, A. and Winter, D.J., On homogeneous spaces and reductive subalgebras of simple Lie algebras, Trans. Amer. Math. Soc., vol. 128 (1967), 142–147.Google Scholar
[10] Spanier, E., Algebraic Topology, McGraw-Hill Company, 1966.Google Scholar
[11] Wolf, J., The geometry and structure of isotropy-irreducible homogeneous spaces, Acta Mathematica, vol. 120 (1968), 59–148.Google Scholar