Skip to main content

Hermitian natural differential operators

  • 628 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1209)

Keywords

  • Maximal Weight
  • Tensor Field
  • Hermitian Manifold
  • Spectral Geometry
  • Kaehler Manifold

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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.

References

  1. M.F. Atiyah, R. Bott and K. Patodi, "On the heat equation and the index theorem" Invent. Math. 19 (1973), 279–330.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. L.A. Cordero, M. Fernández and A. Gray, "Symplectic manifolds with no Kaehler structure", to appear in Topology.

    Google Scholar 

  3. H. Donnelly, "Invariance theory of Hermitian manifolds" Proc. Amer. Math. Soc. 58 (1976), 229–233.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. H. Donnelly, "A spectral condition determining the Kaehler property", Proc. Amer. Math. Soc. 47 (1975), 187–195.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. H. Donnelly, "Heat Equation Asymptotics with Torsion", Indiana Univ. Math. J. Vol. 34 (1985), 105–113.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D.B.A. Epstein, "Natural tensors on Riemannian manifolds", J. Diff. Geom. 10 (1975), 631–635.

    MathSciNet  MATH  Google Scholar 

  7. D.B.A. Epstein and M. Kneser, "Functors between categories of vector spaces", Lecture Notes in Math. Vol. 99 (1969), 154–170.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. A. Ferrández and V. Miquel, "Hermitian natural tensors", Preprint.

    Google Scholar 

  9. P. Gilkey, "curvature and the eigenvalues of the Laplacian for elliptic complexes", Advances in Math. 10 (1973), 344–382.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. P. Gilkey, "Spectral geometry and the Kaehler condition for complex manifolds", Invent, Math. 26 (1974), 231–258, and "Corrections", Invent. Math. 29 (1975), 81–82.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. P. Gilkey, "The spectral geometry of real and complex manifolds", Proc. of Sympos. in Pure Math. Vol. 27 (1975), 265–280.

    CrossRef  MathSciNet  Google Scholar 

  12. P. Gilkey, "Recursion relations and the asymptotic behavior of the eigenvalues of the Laplacian", Compositio Math. 38 (1979), 201–240.

    MathSciNet  MATH  Google Scholar 

  13. A. Gray, "Nearly Kahler manifolds", J. Diff. Geom. 4 (1970), 283–309.

    MATH  Google Scholar 

  14. A. Gray, "The structure of Nearly Kaehler manifolds", Math. Ann. 248 (1976), 233–248.

    CrossRef  MATH  Google Scholar 

  15. A. Gray and L. M. Hervella, "The sixteen classes of almost hermitian manifolds and their linear invariants", Annali di Mat. pura ed applicata IV, vol. XXIII (1980), 35–58.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. H. P. McKean, Jr and I. M. Singer, "Curvature and eigenvalues of the Laplacian", J. Diff. Geom. 1 (1967), 43–69.

    MathSciNet  MATH  Google Scholar 

  17. V. Miquel, "Volumes of certain small geodesic balls and almost hermitian geometry", Geometriae Dedicata 15 (1984), 261–267.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. W. A. Poor, "Differential Geometric Structures", Mc Graw-Hill, Inc., 1981.

    Google Scholar 

  19. P. Stredder, "Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups", J. Diff. Geom. 10 (1975), 647–660.

    MathSciNet  MATH  Google Scholar 

  20. K. Tsukada, "Hopf manifolds and spectral geometry", Trans. Amer. Math. Soc. 270 (1982), 609–621.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Carreras, F.J., Ferrández, A., Miquel, V. (1986). Hermitian natural differential operators. In: Naveira, A.M., Ferrández, A., Mascaró, F. (eds) Differential Geometry Peñíscola 1985. Lecture Notes in Mathematics, vol 1209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076624

Download citation

  • DOI: https://doi.org/10.1007/BFb0076624

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16801-0

  • Online ISBN: 978-3-540-44844-0

  • eBook Packages: Springer Book Archive