Curvature operators: pinching estimates and geometric examples

Jean-Pierre Bourguignon; Hermann Karcher

Annales scientifiques de l'École Normale Supérieure (1978)

  • Volume: 11, Issue: 1, page 71-92
  • ISSN: 0012-9593

How to cite

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Bourguignon, Jean-Pierre, and Karcher, Hermann. "Curvature operators: pinching estimates and geometric examples." Annales scientifiques de l'École Normale Supérieure 11.1 (1978): 71-92. <http://eudml.org/doc/82010>.

@article{Bourguignon1978,
author = {Bourguignon, Jean-Pierre, Karcher, Hermann},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {1},
pages = {71-92},
publisher = {Elsevier},
title = {Curvature operators: pinching estimates and geometric examples},
url = {http://eudml.org/doc/82010},
volume = {11},
year = {1978},
}

TY - JOUR
AU - Bourguignon, Jean-Pierre
AU - Karcher, Hermann
TI - Curvature operators: pinching estimates and geometric examples
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 1
SP - 71
EP - 92
LA - eng
UR - http://eudml.org/doc/82010
ER -

References

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  1. [1] A. BESSE, Manifolds all of whose Geodesics are Closed, Erg. der Math., Springer, 1978. Zbl0387.53010MR80c:53044
  2. [2] J. P. BOURGUIGNON, Sur les formes harmoniques du type de la courbure (C. R. Acad. Sc., Paris, t. 286, 1978, pp. 337-341). Zbl0374.53019MR57 #13782
  3. [3] E. CALABI et E. VESENTINI, On Compact Locally Symmetric Kähler Manifolds (Ann. of Math., Vol. 71, 1960, pp. 472-507). Zbl0100.36002MR22 #1922b
  4. [4] S. GALLOT et D. MEYER, Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne (J. Math. pures et appl., T. 54, 1975, pp. 259-284). Zbl0316.53036MR56 #13128
  5. [5] R. GEROCH, Positive Sectional Curvature does not Imply Positive Gauss-Bonnet Integrand (Proc. A.M.S., Vol. 54, 1976, pp. 267-270). Zbl0325.53042MR52 #11784
  6. [6] S. HELGASON, Differential Geometry and Symmetric Spaces, Academic Press, 1962. Zbl0111.18101MR26 #2986
  7. [7] G. JENSEN, Embeddings of Stiefel Manifolds into Grassmannians (Duke Math. J., Vol. 42, 1975, pp. 397-407). Zbl0335.53042MR51 #11360
  8. [8] H. KARCHER, Pinching implies Strong Pinching (Comment. Math. Helv., Vol. 46, 1971, pp. 124-126). Zbl0216.43803MR45 #1076
  9. [9] T. KATO, Perturbation Theory for Linear Operators, Grund. der math. Wiss., Springer, 1966. Zbl0148.12601MR34 #3324
  10. [10] P. KLEMBECK, On Geroch's Counterexample to the Algebraic Hopf Conjecture (Proc. A.M.S., Vol. 59, 1976, pp. 334-336). Zbl0341.53011MR55 #1250
  11. [11] N. KOISO, Critical Metrics and Non-Deformability of Certain Riemannian Structures (Preprint, 1977). 
  12. [12] R. S. KULKARNI, On the Bianchi Identities (Math. Ann., Vol. 199, 1972, pp. 175-204). Zbl0234.53021MR49 #3767
  13. [13] H. MAILLOT, Sur l'opérateur de courbure d'une variété riemannienne (Thèse de 3e cycle, Université Claude-Bernard, Lyon, 1974). 
  14. [14] A. POLOMBO, Nombres caractéristiques d'une variété riemannienne (Thèse de 3e cycle, Université Paris-VII, 1976). Zbl0339.53041
  15. [15] S. STERNBERG, Lectures on Differential Geometry, Prentice Hall, 1964. Zbl0129.13102MR33 #1797
  16. [16] H. WEYL, Classical Groups, Princeton University Press, Princeton, 1939. JFM65.0058.02

Citations in EuDML Documents

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  1. Dennis M. Deturck, Norihito Koiso, Uniqueness and non-existence of metrics with prescribed Ricci curvature
  2. Hans Jakob Rivertz, On local isometric immersions into complex and quaternionic projective spaces
  3. Hélène Davaux, La K -aire selon M. Gromov
  4. Jean Pierre Bourguignon, L'équation de la chaleur associée à la courbure de Ricci
  5. McKenzie Y. Wang, Wolfgang Ziller, On normal homogeneous Einstein manifolds
  6. Jean-Pierre Bourguignon, Stabilité par déformation non-linéaire de la métrique de Minkowski
  7. J. P. Bourguignon, Première valeur propre du laplacien et volume des sphères riemanniennes
  8. Christoph Böhm, Non-compact cohomogeneity one Einstein manifolds

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