Skip to main content
SpringerLink
Log in
Book cover

Curvature and Topology of Riemannian Manifolds pp 319–336Cite as

Einstein metrics with positive scalar curvature

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1201))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. D. Barden, Simply connected five-manifolds, Ann. of Math. 82 (1965), 365–385.

    Article  MathSciNet  MATH  Google Scholar 

  2. L. Bérard Bergery, Sur des nouvelles variétés riemanniennes d'Einstein, Publications de l'Institut E. Cartan 4, Nancy, (1982), 1–60.

    Google Scholar 

  3. A. Besse, Einstein manifolds, to appear in Springer-Verlag.

    Google Scholar 

  4. A. Borel, Kählerian coset spaces of semisimple Lie groups, Proc. Nat. Acad. Sciences 40 (1954), 1147–1151.

    Article  MathSciNet  MATH  Google Scholar 

  5. J.P. Bourguignon-H. Karcher, Curvature operators: pinching estimates and geometric examples, Ann. Scient. Ecole Normale Supérieure 11 (1978), 71–92.

    MathSciNet  MATH  Google Scholar 

  6. J. D'Atri-W. Ziller, Naturally reductive metrics and Einstein metrics on compact Lie groups, Memoir Amer. Math. Soc. 215 (1979).

    Google Scholar 

  7. E.B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Transl. Amer. Math. Soc. Series 2, Vol. 6 (1957), 111–244.

    Article  MATH  Google Scholar 

  8. A. Futaki: An obstruction to the existence of Einstein Kähler metrics, Inv. Math. 73 (1983), 437–443.

    Article  MathSciNet  MATH  Google Scholar 

  9. N. Hitchin, On compact four dimensional Einstein manifolds, J. Diff. Geom. 9 (1974), 435–442.

    MathSciNet  MATH  Google Scholar 

  10. N. Hitchin, Harmonic spinors, Adv. in Math. 14 (1974), 1–55.

    Article  MathSciNet  MATH  Google Scholar 

  11. G. Jensen, Einstein metrics on principal fibre bundles, J. Diff. Geom. 8 (1973), 599–614.

    MathSciNet  MATH  Google Scholar 

  12. S. Kobayashi, On compact Kähler manifolds with positive definite Ricci tensor, Ann. of Math. 74(1961), 570–774.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. Kobayashi, Topology of positively pinched Kähler manifolds, Tohoku Math. J. 15 (1963), 121–139.

    Article  MathSciNet  MATH  Google Scholar 

  14. N. Koiso-Y. Sakane, Non-homogeneous Kähler Einstein metrics on compact complex manifolds, Preprint 1985.

    Google Scholar 

  15. J.L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Can. J. Math. 7 (1955), 562–576.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Lichnérowicz, Variétés pseudokählerian à courbure de Ricci non nulle; applications aux domaines bornés homogènes de ℂn, C.R. Acad. Sci. Paris 235 (1952), 12–14.

    MathSciNet  MATH  Google Scholar 

  17. A. Lichnérowicz, Spineur harmonique, C.R. Acad. Sci. Paris 257 (1963), 7–9.

    MathSciNet  Google Scholar 

  18. O.V. Manturov, Homogeneous asymmetric Riemannian spaces with an irreducible group of rotations, Dokl. Akad. Nauk. SSSR 141 (1961), 792–795.

    MathSciNet  MATH  Google Scholar 

  19. O.V. Manturov, Riemannian spaces with orthogonal and symplectic groups of motions and an irreducible group of rotations, Dokl. Akad. Nauk. SSSR 141 (1961), 1034–1037.

    MathSciNet  MATH  Google Scholar 

  20. O.V. Manturov, Homogeneous Riemannian manifolds with irreducible isotropy group, Trudy Sem. Vector and Tensor Analysis 13 (1966), 68–145.

    MathSciNet  Google Scholar 

  21. Y. Matsushima, Sur la structure du groupe d'homéomorphismes analytiques d'une certaine variété Kählérienne, Nagoya Math. J. 11 (1957), 145–150.

    MathSciNet  MATH  Google Scholar 

  22. Y. Matsushima, Remarks on Kähler Einstein manifolds, Nagoya Math. J. 46 (1972), 161–173.

    MathSciNet  MATH  Google Scholar 

  23. T. Matsuzawa, Einstein metrics on fibred Riemannian structures, Kodai Math. J. 6 (1983), 340–345.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. Page, A compact rotating gravitational instanton, Phys. Letters 79 B (1979), 235–238.

    MathSciNet  Google Scholar 

  25. D. Page-C.N. Pope, Inhomogeneous Einstein metrics on complex line bundles, Preprint 1985.

    Google Scholar 

  26. Y. Sakane, Examples of compact Kähler Einstein manifolds with positive Ricci tensor, Preprint 1985.

    Google Scholar 

  27. D. Sullivan, Infinitesimal computations in topology, Publ. I.H.E.S. 47 (1977), 269–332.

    Article  MathSciNet  MATH  Google Scholar 

  28. J. Thorpe, Some remarks on the Gauss-Bonnet integral, J. Math. Mech. 18 (1969), 779–786.

    MathSciNet  MATH  Google Scholar 

  29. M. Wang, Some examples of homogeneous Einstein manifolds in dimension seven, Duke Math. J. 49 (1982), 23–28.

    Article  MathSciNet  MATH  Google Scholar 

  30. M. Wang-W. Ziller, On normal homogeneous Einstein manifolds, to appear in Ann. Scient. Ec. Norm. Sup.

    Google Scholar 

  31. M. Wang-W. Ziller, On the isotropy representation of a symmetric space, to appear in Rend. Sem. Mat. Univers. Politecn. Torino.

    Google Scholar 

  32. M. Wang-W. Ziller, Existence and non-existence of homogeneous Einstein metrics, to appear in Inv. Math.

    Google Scholar 

  33. M. Wang-W. Ziller,New examples of Einstein metrics on principal circle bundle, in preparation.

    Google Scholar 

  34. J. Wolf, The geometry and structure of isotropy irreducible homogeneous spaces, Acta. Math. 120 (1968), 59–148.

    Article  MathSciNet  MATH  Google Scholar 

  35. J. Wolf, Correction to "The geometry and structure of isotropy irreducible homogeneous spaces", Acta Math. 152 (1984), 141–142.

    Article  MathSciNet  MATH  Google Scholar 

  36. W. Ziller, Homogeneous Einstein metrics on spheres and projective spaces, Math. Ann. 259 (1982), 351–358.

    Article  MathSciNet  MATH  Google Scholar 

  37. W. Ziller, Homogeneous Einstein metrics, Global Riemannian geometry, ed. Willmore and Hitchin, Ellis Horwood Limited, Chichester 1984, p. 126–135.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut des Hautes Etudes Scientifiques, 35, Rte de Chartres, 91440, Bures-sur-Yvette, France

    M. Wang & W. Ziller

  2. Mc Master University, L85 4K1, Hamilton, Ontario, Canada

    M. Wang

  3. University of Pennsylvania, 19104, Philadelphia, PA, U.S.A.

    W. Ziller

Authors
  1. M. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Ziller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Katsuhiro Shiohama Takashi Sakai Toshikazu Sunada

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Wang, M., Ziller, W. (1986). Einstein metrics with positive scalar curvature. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075665

Download citation

  • DOI: https://doi.org/10.1007/BFb0075665

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16770-9

  • Online ISBN: 978-3-540-38827-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation