Unique decomposition of Riemannian manifolds
Authors:
J.-H. Eschenburg and E. Heintze
Journal:
Proc. Amer. Math. Soc. 126 (1998), 3075-3078
MSC (1991):
Primary 53C20; Secondary 53C12
DOI:
https://doi.org/10.1090/S0002-9939-98-04630-9
MathSciNet review:
1473665
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove an extension of de Rham's decomposition theorem to the non-simply connected case.
- [dR] G. de Rham: Sur la réductibilité d'un espace de Riemann, Comm. Math. Helv. 26 (1952), 328 - 344 MR 14:584a
- [G] M. Gromov, Almost flat manifolds, J. Differential Geometry 13 (1978), no. 2, 231–241. MR 540942
- [KN] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol I, Interscience Publishers, a division of John Wiley & Sons, New York-London, 1963. MR 0152974
- [M] R. Maltz, The de Rham product decomposition, J. Differential Geometry 7 (1972), 161–174. MR 324578
- [P] Radu Pantilie, A simple proof of the de Rham decomposition theorem, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 36(84) (1992), no. 3-4, 341–343. MR 1307730
- [T] Hitoshi Takagi, Notes on the cancellation of Riemannian manifolds, Tohoku Math. J. (2) 32 (1980), no. 3, 411–417. MR 590036, https://doi.org/10.2748/tmj/1178229599
- [U] Kagumi Uesu, Cancellation law for Riemannian direct product, J. Math. Soc. Japan 36 (1984), no. 1, 53–62. MR 723593, https://doi.org/10.2969/jmsj/03610053
Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C20, 53C12
Retrieve articles in all journals with MSC (1991): 53C20, 53C12
Additional Information
J.-H. Eschenburg
Affiliation:
Institut fur Mathematik, Universität Augsburg, D-86135 Augsburg, Germany
Email:
eschenburg@math.uni-augsburg.de
E. Heintze
Affiliation:
Institut fur Mathematik, Universität Augsburg, D-86135 Augsburg, Germany
Email:
heintze@math.uni-augsburg.de
DOI:
https://doi.org/10.1090/S0002-9939-98-04630-9
Keywords:
Riemannian products,
indecomposable Riemannian manifolds,
irreducible Riemannian manifolds,
de Rham's theorem
Received by editor(s):
February 28, 1997
Communicated by:
Christopher Croke
Article copyright:
© Copyright 1998
American Mathematical Society