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Periodica Mathematica Hungarica

, Volume 33, Issue 2, pp 105–113 | Cite as

On three-dimensional conformally flat quasi-Sasakian manifolds

  • Zbigniew Olszak
Article

Abstract

LetM be a 3-dimensional quasi-Sasakian manifold. On such a manifold, the so-called structure function β is defined. With the help of this function, we find necessary and sufficient conditions forM to be conformally flat. Next it is proved that ifM is additionally conformally flat with β = const., then (a)M is locally a product ofR and a 2-dimensional Kählerian space of constant Gauss curvature (the cosymplectic case), or (b)M is of constant positive curvature (the non cosymplectic case; here the quasi-Sasakian structure is homothetic to a Sasakian structure). An example of a 3-dimensional quasi-Sasakian structure being conformally flat with nonconstant structure function is also described. For conformally flat quasi-Sasakian manifolds of higher dimensions see [O1]

Mathematics subject classification numbers, 1991

Primary 53C25 Secondary 53C15 

Key words and phrases

Quasi-Sasakian manifold conformally flat manifold 

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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • Zbigniew Olszak
    • 1
  1. 1.Institute of MathematicsTechnical University of WroclawWroclawPoland

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