Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-23T20:18:44.137Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear invariants of Riemannian almost product manifolds

Published online by Cambridge University Press:  24 October 2008

Francisco J. Carreras
Francisco J. Carreras
Affiliation:
University of Valencia, Spain
Get access Rights & Permissions [Opens in a new window]

Extract

Using the decomposition of a certain vector space under the action of the structure group of Riemannian almost product manifolds, A. M. Naveira (9) has found thirty-six distinguished classes of these manifolds. In this article, we prove that this decomposition is irreducible by computing a basis of the space of invariant quadratic forms on such a space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 1 , January 1982 , pp. 99 - 106
Copyright
Copyright © Cambridge Philosophical Society 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Atiyah, M. F., Bott, R. and Patodi, V. K.On the heat equation and the index theorem. Inventiones Math. 19 (1973), 279–330 (and Errata, 28 (1975), 277–280).CrossRefGoogle Scholar
(2)Berger, M., Gauduchon, P. and Mazet, E.Le spectre d'une variété riemannienne. Lecture Notes in Mathematics no. 194 (Springer-Verlag, 1971).CrossRefGoogle Scholar
(3)Dieudonne, J. and Carrell, J. B.Invariant theory: old and new. (Academic Press, 1971).Google Scholar
(4)Gil-Medrano, O. On the geometric properties of some classes of almost product structures, preprint.Google Scholar
(5)Gray, A.Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 (1967), 715–737.Google Scholar
(6)Gray, A.The volume of a small geodesic ball of a Riemannian manifold. Michigan Math. J. 20 (1973), 329–344.Google Scholar
(7)Gray, A. and Hervella, L. M.The sixteen classes of almost Hermitian manifolds and their linear invariants. Ann. Mat. Pura Appl. 123 (1980), 35–58.CrossRefGoogle Scholar
(8)Montesinos, A. On certain classes of almost product structures, preprint.Google Scholar
(9)Naveira, A. M. A classification of Riemannian almost product manifolds, preprint.Google Scholar
(10)O'neill, B.The fundamental equations of a submersion. Michigan Math. J. 13 (1969), 459–469.Google Scholar
(11)Weyl, H.The classical groups: their invariants and representations. (Princeton University Press, 1946).Google Scholar