Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-03T19:22:50.344Z Has data issue: false hasContentIssue false
  • English
  • Français

On the topological structure of affinely connected manifolds

Published online by Cambridge University Press:  22 January 2016

Tatsuo Higa
Tatsuo Higa*
Affiliation:
Department of Mathematics Faculty of Science, Rikkyo University, Tokyo 171, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of the present paper is to investigate the relationship between the topological structure and differential geometric objects for affinely connected manifolds.

Let M be a compact, connected and oriented Riemannian manifold, Pr(M) the vector space of all parallel r-forms on M and br(M) the r-th Betti number of M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 96 , December 1984 , pp. 41 - 60
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

[ 1 ] Cheeger, J. and Gromoll, D., On the structure of complete manifolds of nonnegative curvature, Ann. of Math., 96 (1972), 413–443.CrossRefGoogle Scholar
[ 2 ] de Rham, G., Sur la réductibilité d’un espace de Riemann, Comment. Math. Helv., 26 (1952), 328–344.CrossRefGoogle Scholar
[ 3 ] de Rham, G., Variétés Differentiates, Hermann, Paris, 1955.Google Scholar
[ 4 ] Eells, J. and Sampson, J. H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109–160.CrossRefGoogle Scholar
[ 5 ] Goldberg, S.I., Curvature and Homology, Academic Press, New York, 1962.Google Scholar
[ 6 ] Greenberg, M.J., Lectures on Algebraic Topology, Benjamin, New York, 1967.Google Scholar
[ 7 ] Higa, T., On a splitting theorem for Riemannian manifolds, to appear in Comment. Math. Univ. St. Paul., (1984).Google Scholar
[ 8 ] Higa, T., On irreducible manifolds and geometric structures, (preprint).Google Scholar
[ 9 ] Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, John Wiley, New York, vol. 1, 1963; vol. 2, 1969.Google Scholar
[10] Nomizu, K., Invariant affine connections on homogeneous spaces, Amer. J. Math., 76 (1954), 33–65.CrossRefGoogle Scholar
[11] Vilms, J., Totally geodesic maps, J. Differential Geom., 4 (1970), 73–79.CrossRefGoogle Scholar