Some regularity theorems in riemannian geometry

Dennis M. Deturck; Jerry L. Kazdan

Annales scientifiques de l'École Normale Supérieure (1981)

  • Volume: 14, Issue: 3, page 249-260
  • ISSN: 0012-9593

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Deturck, Dennis M., and Kazdan, Jerry L.. "Some regularity theorems in riemannian geometry." Annales scientifiques de l'École Normale Supérieure 14.3 (1981): 249-260. <http://eudml.org/doc/82074>.

@article{Deturck1981,
author = {Deturck, Dennis M., Kazdan, Jerry L.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {regularity properties; harmonic coordinates; geodesic normal coordinates; Christoffel symbols; Ricci tensor; Einstein metrics},
language = {eng},
number = {3},
pages = {249-260},
publisher = {Elsevier},
title = {Some regularity theorems in riemannian geometry},
url = {http://eudml.org/doc/82074},
volume = {14},
year = {1981},
}

TY - JOUR
AU - Deturck, Dennis M.
AU - Kazdan, Jerry L.
TI - Some regularity theorems in riemannian geometry
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1981
PB - Elsevier
VL - 14
IS - 3
SP - 249
EP - 260
LA - eng
KW - regularity properties; harmonic coordinates; geodesic normal coordinates; Christoffel symbols; Ricci tensor; Einstein metrics
UR - http://eudml.org/doc/82074
ER -

References

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  1. [BJS] L. BERS, F. JOHN and M. SCHECHTER, Partial Differential Equations, John Wiley, 1964 (later reprinted by Amer. Math. Soc.). Zbl0126.00207MR29 #346
  2. [CH] E. CALABI and P. HARTMAN, On the Smoothness of Isometries (Duke Math. J., Vol. 37, 1970, pp. 741-750). Zbl0203.54304MR44 #957
  3. [C] E. CARTAN, Sur la possibilité de plonger un espace riemannien donné dans un espace euclidien (Ann. Soc. Pol. Math., Vol. 6, 1927, pp. 1-17). Zbl54.0763.05JFM54.0763.05
  4. [D1] D. DETURCK, Metrics With Prescribed Ricci Curvature [Proceedings of I.A.S. Differential Geometry Seminar, 1979-1980 (to appear in Annals of Math. series)]. 
  5. [D2] D. DETURCK, Existence of Metrics With Prescribed Ricci Curvature : Local Theory (to appear). 
  6. [E] A. EINSTEIN, Näherungsweise Integration der Feldgleichungen der Gravitation (S.-B. Preuss. Akad. Wiss., 1916, pp. 688-696). Zbl46.1293.02JFM46.1293.02
  7. [FM] A. FISCHER and J. MARSDEN, General Relativity, Partial Differential Equations, and Dynamical Systems (Proc. Symp. Pure Math., Vol. 28 ; Amer. Math. Soc., 1973, pp. 309-327). Zbl0262.35035MR53 #11656
  8. [GW] R. GREENE and H. WU, Embedding of Open Riemannian Manifolds by Harmonic Functions (Ann. Inst. Fourier, Grenoble, Vol. 25, 1975, pp. 215-235). Zbl0307.31003MR52 #3583
  9. [H] P. HARTMAN, On Geodesic Coordinates (American J. Math., Vol. 73, 1951, pp. 949-954). Zbl0044.17306MR13,683e
  10. [J] M. JANET, Sur la possibilité de plonger un espace riemannien donné dans un espace euclidien (Ann. Soc. Pol. Math., Vol. 5, 1926, pp. 38-42). Zbl53.0699.01JFM53.0699.01
  11. [K] J. KAZDAN, Another Proof of Bianchi's Identity in Riemannian Geometry (to appear in Proc. Amer. Math. Soc., 1981). Zbl0459.53033MR82b:53026
  12. [KW] J. KAZDAN and F. WARNER, Curvature Functions for Open 2-Manifolds (Ann. Math., Vol. 199, 1974, pp. 203-219). Zbl0278.53031MR49 #7950
  13. [KN] S. KOBAYASHI and K. NOMIZU, Foundations of Differential Geometry, Vol. I, Interscience, New York, 1964. Zbl0119.37502
  14. [L] C. LANCZOS, Ein Vereinfachendes Koordinatensystem für die Einsteinschen Gravitationsgleichungen (Phys. Z., Vol. 23, 1922, pp. 537-539). Zbl48.1023.01JFM48.1023.01
  15. [M] B. MALGRANGE, Sur l'intégrabilité des structures presque-complexes (Symposia Math., Vol. II, I.N.D.A.M., Rome, 1968, Academic Press, London, 1969, pp. 289-296). Zbl0186.42504MR40 #6598
  16. [Mo] C. MORREY, Jr., Multiple Integrals in the Calculus of Variations (Grund. der Math. Wiss., Vol. 133, Springer-Verlag, New York, 1966). Zbl0142.38701
  17. [My] S. D. MYERS, Riemannian Manifolds in the Large (Duke Math. J., Vol. 1, 1935, pp. 39-49). Zbl0011.22502JFM61.0786.03
  18. [S] M. SPIVAK, A Comprehensive Introduction to Differential Geometry, Vol. 5, Publish or Perish, 1975. Zbl0306.53003

Citations in EuDML Documents

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  1. Philippe Delanoë, Réarrangements des difféomorphismes sur une variété compacte mesurée
  2. Masanori Kôzaki, On mean value theorems for small geodesic spheres in Riemannian manifolds
  3. Dennis M. DeTurck, The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
  4. Norihito Koiso, Hypersurfaces of Einstein manifolds
  5. Philippe G. LeFloch, Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
  6. Stefan Peters, Convergence of riemannian manifolds
  7. Andrzej Derdziński, Self-dual Kähler manifolds and Einstein manifolds of dimension four
  8. Jean Pierre Bourguignon, L'équation de la chaleur associée à la courbure de Ricci

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