Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-02-05T15:12:33.636Z Has data issue: false hasContentIssue false
  • English
  • Français

A characterization of locally homogeneous Riemann manifolds of dimension 3

Published online by Cambridge University Press:  22 January 2016

Kazuo Yamato
Kazuo Yamato*
Affiliation:
Department of Mathematics, College of General Education Nagoya University, Chikusa-ku, Nagoya 464-01, 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.

It is classical to characterize locally homogeneous Riemann manifolds by infinitesimal conditions. For example, [Si] asserts that the local-homogeneity is equivalent to the existence of linear isometries between tangent spaces which preserve the curvatures and their covariant derivatives up to certain orders. It is also known that the local homogeneity is equivalent to the existence of a certain tensor field of type (1, 2) (for this and a further study, see [TV]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 77 - 90
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[KTV] Kowalski, O., Tricerri, F. and Vanhecke, L., Curvature homogeneous Riemannian manifolds, preprint.Google Scholar
[M] Milnor, J., Curvatures of left invariant metrics on Lie groups, Advances in Math., 21 (1976), 293–329.Google Scholar
[O] O’Neill, B., The fundamental equations of a submersion, Michigan Math. J., 13 (1966), 459–469.Google Scholar
[Se] Sekigawa, K., On some 3-dimensional Riemannian manifolds, Hokkaido Math. J., 2 (1973), 259–270.CrossRefGoogle Scholar
[Si] Singer, I. M., Infinitesimally homogeneous spaces, Comm. Pure Appl. Math., 13 (1960), 685–697.Google Scholar
[T] Takagi, H., On curvature homogeneity of Riemannian manifolds, Tôhoku Math. J., 26 (1974), 581–585.Google Scholar
[TV] Tricerri, F. and Vanhecke, L., Curvature homogeneous Riemannian manifolds, Ann. Sci. École Norm. Sup., 22 (1989), 535–554.Google Scholar