On pinched manifolds with fundamental group 𝐙 2

Karsten Grove; Hermann Karcher

Compositio Mathematica (1973)

  • Volume: 27, Issue: 1, page 49-61
  • ISSN: 0010-437X

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Grove, Karsten, and Karcher, Hermann. "On pinched manifolds with fundamental group $\mathbf {Z}_2$." Compositio Mathematica 27.1 (1973): 49-61. <http://eudml.org/doc/89179>.

@article{Grove1973,
author = {Grove, Karsten, Karcher, Hermann},
journal = {Compositio Mathematica},
language = {eng},
number = {1},
pages = {49-61},
publisher = {Noordhoff International Publishing},
title = {On pinched manifolds with fundamental group $\mathbf \{Z\}_2$},
url = {http://eudml.org/doc/89179},
volume = {27},
year = {1973},
}

TY - JOUR
AU - Grove, Karsten
AU - Karcher, Hermann
TI - On pinched manifolds with fundamental group $\mathbf {Z}_2$
JO - Compositio Mathematica
PY - 1973
PB - Noordhoff International Publishing
VL - 27
IS - 1
SP - 49
EP - 61
LA - eng
UR - http://eudml.org/doc/89179
ER -

References

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  1. [1 ] M. Berger: Les variétés riemanniennes à courbure positive. Bull. Soc. Math. Belgique.10 (1958) 89-104. Zbl0096.15501
  2. [2] M. Berger: An extension of Rauch's metric comparison theorem and some applications. Illinois J. of Math., 6 (1962) 700-712. Zbl0113.37003MR143159
  3. [3] J. Cerf: Sur les difféomorphismes de la sphère de dimension trois (Γ4 = 0). Springer Lecture Notes, series 53 (1968). Berlin-Heidelberg -New York. Zbl0164.24502
  4. [4] D. Gromoll: Differenzierbare Strukturen und Metriken positiver Krümmung auf Sphären. Math. Ann., 164 (1966) 353-371. Zbl0135.40301MR196754
  5. [5] D. Gromoll, W. Klingenberg, W. Meyer: Riemannsche Geometrie im Grossen. Springer Lecture Notes, series 55 (1968). Berlin-Heidelberg-New York. Zbl0155.30701MR365399
  6. [6] K. Grove: Condition (C) for the energy integral on certain path-spaces and applications to the theory of geodesics. J. Diff. Geom (to appear). Zbl0277.58004MR339270
  7. [7] K. Grove: Isometry-invariant geodesics (preprint Bonn). MR370651
  8. [8] K. Grove, H. Karcher: How to conjugate C1-close group actions. Math. Z., 132 (1973) 11-20. Zbl0245.57016MR356104
  9. [9] M. Kervaire, J. Milnor: Groups of homotopy Spheres I. Ann. of Math., 77 (1963) 504-537. Zbl0115.40505MR148075
  10. [10] W. Klingenberg: Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung. Comment. Math. Helv., 35 (1961) 35-54. Zbl0133.15005MR139120
  11. [11] G.R. Livesay: Fixed point free involutions on the 3-sphere. Ann. of Math., 72 (1960) 603-611. Zbl0096.17302MR116343
  12. [12] S. Lopez De Medrano: Involutions on manifolds. Springer Verlag (1971) Berlin- Heidelberg-New York. Zbl0214.22501MR298698
  13. [13] E.A. Ruh: Krümmung und differenzierbare Strukturen auf Sphären, IIMath. Ann., 205 (1973) 113-129. Zbl0273.53035MR370429
  14. [14] K. Shiohama: The diameter of δ-pinched manifolds. J. Diff. Geom., 5 (1971) 61-74. Zbl0218.53062
  15. [15] K. Shiohama, M. Sugimoto, H. Karcher: On the differentiable pinching problem. Math. Ann., 195 (1971) 1-16. Zbl0214.48902MR290291

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