Uniqueness and non-existence of metrics with prescribed Ricci curvature

Dennis M. Deturck; Norihito Koiso

Annales de l'I.H.P. Analyse non linéaire (1984)

  • Volume: 1, Issue: 5, page 351-359
  • ISSN: 0294-1449

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Deturck, Dennis M., and Koiso, Norihito. "Uniqueness and non-existence of metrics with prescribed Ricci curvature." Annales de l'I.H.P. Analyse non linéaire 1.5 (1984): 351-359. <http://eudml.org/doc/78080>.

@article{Deturck1984,
author = {Deturck, Dennis M., Koiso, Norihito},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ricci tensor; Levi-Civita connection},
language = {eng},
number = {5},
pages = {351-359},
publisher = {Gauthier-Villars},
title = {Uniqueness and non-existence of metrics with prescribed Ricci curvature},
url = {http://eudml.org/doc/78080},
volume = {1},
year = {1984},
}

TY - JOUR
AU - Deturck, Dennis M.
AU - Koiso, Norihito
TI - Uniqueness and non-existence of metrics with prescribed Ricci curvature
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 5
SP - 351
EP - 359
LA - eng
KW - Ricci tensor; Levi-Civita connection
UR - http://eudml.org/doc/78080
ER -

References

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  1. [Be] A. Besse, Géométrie riemannien en dimension 4, Cedic Fernand Nathan, Paris, 1981. MR769127
  2. [BK] J. Bourguignon and H. Karcher, « Curvature operators: pinching estimates and geometric examples », Ann. Scient. Ec. Norm. Sup., 4e série, t. 11, 1978, p. 71-92. Zbl0386.53031MR493867
  3. [C1] E. Calabi, « Extremal Kähler metrics », in Seminar on Differential Geometry, S. T. Yau, ed., Annals of Math Study 102, Princeton U. Press, 1982, p. 259-290. Zbl0487.53057MR645743
  4. [C2] E. Calabi, « Métriques Kählériennes et fibrés holomorphes », Ann. Sci. Ec. Norm. Sup., 4e série, t. 12, 1979, p. 269-294. Zbl0431.53056MR543218
  5. [D] D. Deturck, « Metrics with prescribed Ricci curvature » in Seminar on Differential Geometry, S. T. Yau ed., Annals of Math Study 102, Princeton U. Press, 1982, p. 525-537. Zbl0478.53031MR645758
  6. [EL] J. Eells and L. Lemaire, « A report on harmonic maps », Bull. London Math. Soc., t. 10, 1978, p. 1-68. Zbl0401.58003MR495450
  7. [H] R. Hamilton, The Ricci curvature equation, preprint, MSRIBerkeley, 1983. MR765228
  8. [KN1] S. Kobayashi and K. Nomizu, Foundations of DifferentialGeometry, vol. 1, Wiley-Interscience, New York, 1963. Zbl0119.37502MR152974
  9. [KN2] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. 2, Wiley-Interscience, New York, 1969. Zbl0175.48504MR238225
  10. [M] J. Milnor, « Curvatures of left-invariant metrics on Lie groups », Adv. in Math., t. 21, 1976, p. 293-329. Zbl0341.53030MR425012

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