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Integrable spreads and spaces of constant curvature

  • H. R. Farran (a1) and S. A. Robertson (a2)

Synopsis

This paper is a continuation of [2], where we introduced the notion of global k-spreads on manifolds. Here we show that the space of all k-spreads on a manifold has the structure of an affine space, modelled on the vector space of sections of a certain vector bundle. We give some sufficient conditions for a manifold admitting an integrable k-spread to be a space of constant curvature and answer one of the questions raised in [2].

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References

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1Cartan, É.. Leçons sur La Géométrie des éspaces de Riemann (Paris: Gauthier-Villars, 1946).
2Farran, H. R. and Robertson, S. A.. Integrable Spreads. Proc. Roy. Soc. Edinburgh Seel A. 96 (1984), 206210.
3Kobayashi, S. and Nomizu, K.. Foundations of Differential Geometry, Vol. I (New York: Interscience, 1963).
4Leung, D. S. and Nomizu, K.. The axiom of spheres in Riemannian Geometry. J. Differential Geometry 5 (1971), 487489.
5Spivak, M.. A Comprehensive Introduction to Differential Geometry Vol. 4 (Boston: Publish or Perish, 1975).

Integrable spreads and spaces of constant curvature

  • H. R. Farran (a1) and S. A. Robertson (a2)

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