On the Geometry of Conformal Anti-invariant $\xi^\perp-$ Submersions

  • Mehmet Akif Akyol Bingol University
  • Yılmaz Gündüzalp Dicle University
Keywords: Almost contact metric manifold, conformal submersion, anti-invariant $\xi^\perp-$ Riemannian submersion, conformal anti-invariant $\xi^\perp-$submersion


Lee [Anti-invariant $\xi^{\perp}-$ Riemannian submersions from almost contact manifolds, Hacettepe Journal of Mathematics and Statistic, 42(3), (2013), 231-241.] defined and studied anti-invariant $\xi^\perp-$ Riemannian submersions from almost contact manifolds.
The main goal of this paper is to consider conformal anti-invariant $\xi^\perp-$ submersions (it means the Reeb vector field $\xi$ is a horizontal vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of anti-invariant $\xi^\perp-$ Riemannian submersions. More precisely, we obtain the geometries of the leaves of $\ker\pi_{*}$ and $(\ker\pi_{*})^\perp,$ including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^\perp-$ submersion.