Skip to main content
Log in

Einstein-like manifolds which are not Einstein

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Berger, M., Gauduchon, P. and Mazet, E., ‘Le spectre d'une variété riemannienne’, Lecture Notes in Mathematics, Vol. 194, Springer Verlag, Berlin and New York, 1971.

    Google Scholar 

  2. Berger, M. and Ebin, D.J., ‘Some Decompositions on the Space of Riemannian Manifolds’, J. Diff. Geom. 3, 379–392 (1969).

    MATH  Google Scholar 

  3. Bourguignon, J.P., ‘On Harmonic Forms of Curvature Type’, (to appear).

  4. Chaki, M. C. and Gupta, B., ‘On Conformally Symmetric Spaces’, Indian J. Math. 5, 113–122 (1963).

    Google Scholar 

  5. Cheng, S.Y. and Yau, S.T., ‘Hypersurfaces with Constant Scalar Curvature’, Math. Ann. 225, 195–204 (1977).

    Google Scholar 

  6. Glodek, E., ‘Some Remarks on Conformally Symmetric Riemannian Spaces’, Coll. Math. 23, 121–123 (1971).

    Google Scholar 

  7. Goldberg, S.I., ‘On Conformally Flat Spaces with Definite Ricci Curvature’, Kodai Math. Sem. Rep. 21, 226–232 (1969).

    Google Scholar 

  8. Goldberg, S.I. and Okumura, M., ‘Conformally Flat Manifolds and a Pinching Problem on the Ricci Tensor’, Proc. Am. Math. Soc. 58, 234–236 (1976).

    Google Scholar 

  9. Gray, A., ‘Pseudo-Riemannian Almost Product Manifolds and Submersions’, J. Math. Mech. 16, 715–737 (1967).

    Google Scholar 

  10. Gray, A., ‘Nearly Kähler Manifolds’, J. Diff. Geom. 4, 283–310 (1970).

    Google Scholar 

  11. Gray, A., ‘Riemannian Manifolds with Geodesic Symmetries of Order 3’, J. Diff. Geom. 7, 343–369 (1972).

    Google Scholar 

  12. Gray, A., ‘Compact Kähler Manifolds with Nonnegative Sectional Curvature’, Invent. Math. 41, 33–43 (1977).

    Google Scholar 

  13. Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, John Wiley, New York, 1961.

    Google Scholar 

  14. Matsushima, Y., ‘Remarks on Kähler-Einstein Manifolds’, Nagoya Math. J. 46, 161–173 (1972).

    Google Scholar 

  15. Nomizu, K., ‘Invariant Affine Connections on Homogeneous Spaces’, Am. J. Math. 76, 33–65 (1954).

    Google Scholar 

  16. Nomizu, K., ‘On the Decomposition of Generalized Curvature Tensor Fields’, Differential Geometry in Honor of K. Yano, Kinokunuja, Tokyo, pp. 335–345 (1972).

    Google Scholar 

  17. Nomizu, K. and Smythe, B., ‘A Formula of Simons' Type and Hypersurfaces with Constant Mean Curvature’, J. Diff. Geom. 3, 367–377 (1969).

    Google Scholar 

  18. Ryan, P., ‘A Note on Conformally Flat Spaces with Constant Scalar Curvature’, Proc. 13th Biennial Seminar of the Canadian Math. Congress.

  19. Schouten, J.A., ‘Ricci Calculus, Der mathematischen Wissenschaften’ in Einzeldarstellungen, Band X, Springer Verlag, Berlin, 1954.

    Google Scholar 

  20. Simon, U., ‘Compact Conformally Symmetric Riemannian Spaces’, Math. Z. 132, 173–177 (1973).

    Google Scholar 

  21. Simon, U., ‘On Differential Operators of Second Order on Riemannian Manifolds with Nonpositive Curvature’, Coll. Math. 31, 223–229 (1974).

    Google Scholar 

  22. Sumitomo, T., ‘On a Certain Class of Riemannian Homogeneous Spaces’, Coll. Math. 26, 129–133 (1972).

    Google Scholar 

  23. Tani, M., ‘On a conformally Flat Riemannian Space with Positive Ricci Curvature’, Tôhoku Math. J. 19, 227–231 (1967).

    Google Scholar 

  24. Wegner, B., ‘Codazzi-Tensoren und Kennzeichnungen sphärischer Immersionen’, J. Diff. Geom. 9, 61–70 (1974).

    Google Scholar 

  25. Wegner, B., ‘Kennzeichnungen von Räumen konstanter Krümmung unter local konformeuklidischen Riemannschen Mannigfaltigkeiten’, Geom. Dedicata (to appear).

  26. Yano, K., Integral Formulas in Riemannian Geometry, Marcel Dekker, Inc., New York, 1970.

    Google Scholar 

  27. Yano, K. and Bochner, S., ‘Curvature and Betti Numbers’, Ann. Math. Studies 32, Princeton University Press, Princeton, New Jersey, 1953.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gray, A. Einstein-like manifolds which are not Einstein. Geom Dedicata 7, 259–280 (1978). https://doi.org/10.1007/BF00151525

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00151525

Navigation