Conformal changes of riemannian metrics satisfying certain conditions

  • Kentaro Yano
  • Hitosi Hiramatu


The authors try to find necessary and sufficient conditions for the existence of conformal changes of metrics of Riemannian manifolds which implies that the Riemannian manifolds are isometric to spheres. They first obtain a series of integral inequalities in Riemannian manifolds relative to conformal changes of metrics and then find necessary and sufficient conditions under which the Riemannian manifolds are isometric to spheres.


Conformal Change Riemannian Manifold Integral Inequality Riemannian Metrics 
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  1. [1]
    S. I. Golgberg -K. Yano,Manifolds admitting a non-homothetic conformal transformation, Duke Math. J.,37 (1970), pp. 655–670.CrossRefMathSciNetGoogle Scholar
  2. [2]
    M. Kurita,A note on conformal mappings of certain Riemannian manifolds, Nagoya Math. J.,21 (1962), pp. 111–114.zbMATHMathSciNetGoogle Scholar
  3. [3]
    M. Obata,Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan,14 (1962), pp. 333–340.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Y. Tashiro,Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc.,117 (1965), pp. 251–275.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    K. Yano,Integral formulas in Riemannin geometry, Marcel Dekker, Inc., New York, 1970.Google Scholar
  6. [6]
    K. Yano -H. Hiramatu,On conformal changes of Riemannian metrics, Kodai Math. Sem. Rep.,27 (1976), pp. 19–41.MathSciNetzbMATHGoogle Scholar
  7. [7]
    K. Yano - H. Hiramatu,On isometry of Riemannian manifolds to spheres, to appear in J. of Differential Geometry.Google Scholar
  8. [8]
    K. Yano -M. Obata,Conformal changes of Riemannian metrics, J. of Differential Geometry,4 (1970), pp. 53–72.MathSciNetzbMATHGoogle Scholar
  9. [9]
    K. Yano -S. Sawaki,Riemannian manifolds admitting a conformal transformation group, J. of Differential Geometry,2 (1968), pp. 161–184.MathSciNetzbMATHGoogle Scholar
  10. [10]
    K. Yano -S. Sawaki,Notes on conformal changes of Riemannian metrics, Ködai Math. Sem. Rep.,22 (1970), pp. 480–500.MathSciNetzbMATHGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1977

Authors and Affiliations

  • Kentaro Yano
    • 1
  • Hitosi Hiramatu
    • 2
  1. 1.TokyoJapan
  2. 2.KumamotoJapan

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