Advertisement

Curvature Properties of Para-Kähler Manifolds

  • E. Garcia-Rio
  • L. Hervella
  • R. Vásquez-Lorenzo
Part of the Mathematics and Its Applications book series (MAIA, volume 350)

Abstract

We present some results on the curvature of para-Kähler manifolds. Special attention is paid on the behaviour of the paraholomorphic sectional curvature on degenerate planes.

Mathematics Subject Classification

53C15 53C35 53C50. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Bonome, R. Castro, E. García-Río, L. Hervella, On the holomorphicsectional curvature of an indefinite Kähler manifold, Compt. Rend. Acad. Sci. Paris 315 (1992), 1183–1187.zbMATHGoogle Scholar
  2. 2.
    A. Bonome, R. Castro, E. García-Río, L. Hervella, Y. Matsushita, Null holomorphica Uy flat indefinite almost Hermitian manifolds, Illinois J. Math., (to appear).Google Scholar
  3. 3.
    J. Cendan-Verdes, E. García-Río, M.E. Vázquez-Abal, On the semi-Riemannian structure of the tangent bundle to a two-point homogeneous space, Riv. Mat. Univ. Parma, (to appear).Google Scholar
  4. 4.
    V. Cruceanu, P. Fortuny, P.M. Gadea, Para-Hermitian and para-Kähler manifolds, Bull. Soc. Math. Belg., (to appear)Google Scholar
  5. 5.
    M. Dajczer, K. Nomizu, On sectional curvature of indefinite metrics II, Math. Ann., 247 (1980), 279–282.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    P.M. Gadea, A. Montesinos, Spaces of constant paraholomorphic sectional curvature, Pacific J. Math., 136 (1989), 85–101.MathSciNetzbMATHGoogle Scholar
  7. 7.
    P.M. Gadea, A. Montesinos, Some geometric properties of paraKählerian space forms, Rend. Sem. Mat. Univ. Cagliari, 59 (1989), 85–101.Google Scholar
  8. 8.
    P.M. Gadea, J. Muñoz, Classification of almost parahermitian manifolds, Rend. Mat., 11 (1991), 377–396.zbMATHGoogle Scholar
  9. 9.
    L. Graves, K. Nomizu, On sectional curvature of indefinite metrics, Math. Ann., 232 (1978), 267–272.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    R.S. Kulkarni, The values of sectional curvature in indefinite metrics, Comm. Math. Helv., 54 (1979), 173–176.zbMATHCrossRefGoogle Scholar
  11. 11.
    K. Nomizu, Remarks on sectional curvature of an indefinite metric, Proc. Amer. Math. Soc., 89 (1983), 473–476.MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    J.A. Thorpe, Curvature and the Petrov canonical forms, J. Math. Phys., 10 (1969), 1–7.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    R. Vázquez-Lorenzo, Curvatura de variedades para-Kählerianas, Publ. Dep. Geometría y Topologfa, 82, 1994.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • E. Garcia-Rio
    • 1
  • L. Hervella
    • 2
  • R. Vásquez-Lorenzo
    • 2
  1. 1.Departamento de Análise Matemática, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiagoSpain
  2. 2.Departamento de Xeometría e Topoloxía, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiagoSpain

Personalised recommendations