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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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New invariant Einstein metrics on generalized flag manifolds
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by Andreas Arvanitoyeorgos PDF
Trans. Amer. Math. Soc. 337 (1993), 981-995 Request permission

Abstract:

A generalized flag manifold (or a Kählerian $C$-space) is a homogeneous space $G/K$ whose isotropy subgroup $K$ is the centralizer of a torus in $G$. These spaces admit a finite number of Kähler-Einstein metrics. We present new non-Kahler Einstein metrics for certain quotients of $U(n)$, $SO(2n)$ and ${G_2}$. We also examine the isometry question for these metrics.
References
    A. Arvanitoyeorgos, Invariant Einstein metrics on homogeneous spaces, Ph.D. thesis, University of Rochester, 1991.
  • D. V. Alekseevski, Homogeneous Einstein metrics, Differential geometry and its applications, communications (Brno, 1986) Univ. J. E. Purkyně, Brno, 1987, pp. 1–21. MR 923361
  • D. V. Alekseevskiĭ and A. M. Perelomov, Invariant Kähler-Einstein metrics on compact homogeneous spaces, Funktsional. Anal. i Prilozhen. 20 (1986), no. 3, 1–16, 96 (Russian). MR 868557
  • Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
  • M. Bordemann, M. Forger, and H. Römer, Homogeneous Kähler manifolds: paving the way towards new supersymmetric sigma models, Comm. Math. Phys. 102 (1986), no. 4, 605–617. MR 824094
  • M. A. Guest, Geometry of maps between generalized flag manifolds, J. Differential Geom. 25 (1987), no. 2, 223–247. MR 880184
  • S. Kobayashi and K. Nomizu, Foundations of differential geometry. II, Wiley, New York, 1969.
  • Masahiro Kimura, Homogeneous Einstein metrics on certain Kähler $C$-spaces, Recent topics in differential and analytic geometry, Adv. Stud. Pure Math., vol. 18, Academic Press, Boston, MA, 1990, pp. 303–320. MR 1145261, DOI 10.2969/aspm/01810303
  • Yosi\B{o} Mut\B{o}, On Einstein metrics, J. Differential Geometry 9 (1974), 521–530. MR 362143
  • Arthur A. Sagle and Ralph E. Walde, Introduction to Lie groups and Lie algebras, Pure and Applied Mathematics, Vol. 51, Academic Press, New York-London, 1973. MR 0360927
  • V. S. Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0376938
  • Nolan R. Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. of Math. (2) 96 (1972), 277–295. MR 307122, DOI 10.2307/1970789
  • Zhe Xian Wan, Lie algebras, International Series of Monographs in Pure and Applied Mathematics, Vol. 104, Pergamon Press, Oxford-New York-Toronto, Ont., 1975. Translated from the Chinese by Che Young Lee. MR 0412238
  • Hsien-Chung Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math. 76 (1954), 1–32. MR 66011, DOI 10.2307/2372397
  • McKenzie Y. Wang and Wolfgang Ziller, On normal homogeneous Einstein manifolds, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 4, 563–633. MR 839687
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 337 (1993), 981-995
  • MSC: Primary 53C25; Secondary 53C30
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1097162-3
  • MathSciNet review: 1097162