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Journal of Mathematical Sciences

, Volume 208, Issue 1, pp 115–130 | Cite as

Transverse Equivalence of Complete Conformal Foliations

  • N. I. ZhukovaEmail author
Article
  • 21 Downloads

We study the problem of classification of complete non-Riemannian conformal foliations of codimension q > 2 with respect to transverse equivalence. It is proved that two such foliations are transversally equivalent if and only if their global holonomy groups are conjugate in the group of conformal transformations of the q-dimensional sphere Conf (\( {\mathbb{S}}^{\mathrm{q}} \)). Moreover, any countable essential subgroup of the group Conf (\( {\mathbb{S}}^{\mathrm{q}} \)) is realized as the global holonomy group of some non-Riemannian conformal foliation of codimension q. Bibliography: 16 titles.

Keywords

Manifold Riemannian Manifold Conformal Transformation Global Attractor Canonical Projection 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsNizhny NovgorodRussia

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