This work was done under the program "Sonderforschungsbereich Theorethische Mathematik" at Bonn. Discussions with Gromov during the Arbeitstagung 1977 were very helpfull. Since early 1978 I am working jointly with Peter Buser.
Preview
Unable to display preview. Download preview PDF.
Literature
A. D. ALEXANDROW-Metrische Räume mit einer Krümmung nicht grösser als K, In: Der Begriff des Raumes in der Geometrie, Bericht von der Riemanntagung 1957.
P. BUSER und H. KARCHER-Diskrete Gruppen und kleine Krümmung nach Gromov, to appear.
J. CHEEGER, D. EBIN-Comparison Theorems in Riemannian Geometry, North-Holland Math. Library, New York, 1975.
K. GROVE, H. KARCHER, E. RUH-Finsler Metrics on Compact Lie Groups with an Application to Differentiable Pinching Problems, Math. Ann., 211 (1974), p. 7–21.
D. GROMOLL, W. KLINGENBERG, W. MEYER-Riemannsche Geometrie im Grossen, Lecture Notes in Math., no 55, Springer Verlag, Berlin, 1968.
M. GROMOV-Almost Flat Manifolds, Journ. Diff. Geom., to appear.
M. GROMOV-Manifolds of Negative Curvature, to appear.
E. HEINTZE-Mannigfaltigkeiten negativer Krümmung, Habilitationsschrift, Bonn, 1976.
H. KARCHER-Riemannian Center of Mass and Mollifier Smoothing, C.P.A.M., Vol. XXX, p. 509–541, 1977.
S. KOBAYASHI, K. NOMIZU-Foundations of Differential Geometry I, John Wiley and Sons, New York-London, 1963.
A. I. MAL'CEV-On a Class of Homogeneous Spaces, Izvestiya Akad. Nauk SSSR, Ser. Mat. 13, 9–32 (1949), translated in: Lie groups, AMS Transl. Series 1, vol. 9 (1962).
J. WOLF-Spaces of Constant Curvature, McGraw-Hill, New York, 1967.
Rights and permissions
Copyright information
© 1980 N. Bourbaki
About this paper
Cite this paper
Karcher, H. (1980). Report on M. Gromov's almost flat manifolds. In: Séminaire Bourbaki vol. 1978/79 Exposés 525 – 542. Lecture Notes in Mathematics, vol 770. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0096233
Download citation
DOI: https://doi.org/10.1007/BFb0096233
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09733-4
Online ISBN: 978-3-540-38547-9
eBook Packages: Springer Book Archive