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Riemannian Structures Subordinate to Certain Almost Tangent Structures

Published online by Cambridge University Press:  20 November 2018

M. P. Closs
M. P. Closs*
Affiliation:
University of Ottawa, Ottawa, Ontario
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Almost tangent structures have been studied by Eliopoulos [1] and certain Riemannian structures subordinate to almost tangent structures have been studied by Closs [2]. In this paper we investigate those subordinate Riemannian structures for which the underlying almost tangent structure is without torsion and those for which the fundamental form is closed.

Similar studies have been carried out with respect to Riemannian structures subordinate to almost complex structures by Lichnerowicz [4] and with respect to Riemannian structures subordinate to almost product structures by Legrand [5].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 71 - 77
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Eliopoulos, H. A., On the general theory of differentiable manifolds with almost tangent structure, Canad. Math. Bull. (6) 8 (1965), 721-748.Google Scholar
2. Closs, M. P., On real almost hermitian structures subordinate to almost tangent structures, Canad. Math. Bull. (1) 11 (1968), 115-133.Google Scholar
3. Closs, M. P., Les opérateurs C et M sur les variétés r-tangentes, C. R. Acad. Sci. Paris 267 (1968), 28-31.Google Scholar
4. Lichnerowicz, A., Théorie globale des connexions et des groupes d'holonomie, Edizioni Cremonese, Rome, 1962.Google Scholar
5. Legrand, G., Etude d'une generalization des structures presque complexes sur les variétés différentiables, Thèse, Rend. Cire. Mat. Palermo, Serie2 VII (1958), 323-354; Vin(1959) 5-48.Google Scholar
6. Mme., Lehmann-Lejeune, Intégrabilité des G-structures définies par une 1-forme 0-deformable ? valeurs dans le fibre tangent, Ann. Inst. Fourier (Grenoble) 16 (1968), 329-387.Google Scholar