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On the Spheres Carrying an Almost Contingent Structure

Published online by Cambridge University Press:  20 November 2018

K. L. Duggal
K. L. Duggal*
Affiliation:
Department of Mathematics, University of Windsor, Windsor, Ontario, Canada
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It is well-known that odd dimensional spheres carry a normal contact structure [6], Blair, Ludden and Yano [2] have recently studied a more general structure whose non-trivial example is an even dimensional sphere. Recently, the present author introduced the notion of almost contingent structures [8] with a view to develop a unified theory of various existing structures on a differentiable manifold. It is the purpose of this paper to show that even as well as odd dimensional spheres carry an almost contingent structure. In the sequel, each manifold introduced is C∞, arcwise connected and satisfies the second axiom of countability.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 195 - 201
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Walker, A. G., Almost product structure, Proceedings of the third symposium in pure mathematics of the A.M.S., 3 (1961), 94-100.Google Scholar
2. Blair, D. E., Ludden, G. D. and Yano, K., Induced structures on submanifolds, Kôdai Math. Rep. 22 (1970), 188-198.Google Scholar
3. Yano, K. and Okumura, M., On (f,g, u, v, λ-structures, Kōdai Math. Sem. Rep. 22 (1970), 401-423.Google Scholar
4. Okumura, M., Totally umbilical submanifolds of a Kählerian manifold, J. Math. Soc. Japan 19 (1967), 317-327.Google Scholar
5. Blair, D. E., Geometry of manifolds with structural group U(n) X O(s),J. Diff Geom. 4 (1970), 155-167.Google Scholar
6. Ludden, G. D.,Submanifolds of cosymplectic manifolds, J. Diff. Geom., 4 (1970),237-244.Google Scholar
7. Tashiro, Y., On contact structure ofhyper surfaces in complex manifolds 1, Tohoku Math. J., 15 (1963), 62-78.Google Scholar
8. Duggal, K. L., On a unified theory of differentiable structures, I: almost contingent structures, Tensor, N.S. 25 (1972), 303-308.Google Scholar
9. Duggal, K. L. On a unified theory of differentiable structures, II:Existence theorems, Tensor, N.S. 29 (1975).Google Scholar