Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T07:27:51.279Z Has data issue: false hasContentIssue false
  • English
  • Français

On Real Almost Hermitian Structures Subordinate to Almost Tangent Structures

Published online by Cambridge University Press:  20 November 2018

Mike P. Closs
Mike P. Closs*
Affiliation:
University of Ottawa
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.

Some of the most important G-structures of the first kind (1) are those defined by linear operators satisfying algebraic relations. Let J be a linear operator acting on the complexified space of a differentiable manifold V, and satisfying a relation of the form

where λ is a complex constant and I is the identity operator. In the case λ ≠ 0 the manifold has an almost product structure (2) which in the case λ = i reduces to an almost complex structure (3). In the remaining case, λ = 0, the manifold has an almost tangent structure (4).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 1 , April 1968 , pp. 115 - 133
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bernard, D., Sur la géométrie différentielle des G-structures; Ann. Inst. Fourier; Grenoble 10; 1960, pp. 153-273.10.5802/aif.99Google Scholar
2. Legrand, G., Etude d'une généralization des structures presque complexes sur les variétés différentiables; Thèse;Rendiconti del Circolo Matematico di Palermo; Série 2; T. VII-1958, pp. 323-354; T. VIII-1959, pp. 5–48.Google Scholar
3. Ldchnerowicz, A., Théorie globale des connexions et des groupes dfholonomie; Edizioni Cremonese, Roma; 1962.Google Scholar
4. Eliopoulos, H. A., On the general theory of differentiable manifolds with almost tangent structure; Canad. Math. Bull. vol. 8, no. 6, 1965, pp. 721-748.10.4153/CMB-1965-054-5Google Scholar
5. Klein, J., Opérateurs différentiels sur les variétés presque tangents; C. R. Acad. Sc., Paris; t-257, 1963, pp. 2392-2394.Google Scholar
6. Eliopoulos, H. A., Euclidean structures compatible with almost tangent structures; Bull. de l'acad. Royale de Belgique (Classe des Sc.,); 5e Série - tome L; 1964–10; pp. 1174-1182.Google Scholar
7. Schwerdtfeger, H., Introduction to linear algebra and the theory of matrices; 2nd edition, P. Noordhoff, N. V. - 1961, Groningen.Google Scholar