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

#### International Journal of Maps in Mathematics - IJMM

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 Field Value Title On the Geometry of Conformal Anti-invariant $\xi^\perp-$ Submersions Creator Akyol, Mehmet Akif Gündüzalp, Yılmaz Description 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. Publisher Bayram Şahin Date 2018-04-24 Type info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Format application/pdf Identifier http://www.journalmim.com/index.php/ijmm/article/view/4 Source International Journal of Maps in Mathematics - IJMM; Vol 1 No 1 (2018): International Journal of Maps in Mathematics; 50-67 2636-7467 Language eng Relation http://www.journalmim.com/index.php/ijmm/article/view/4/4 Rights Copyright (c) 2018 International Journal of Maps in Mathematics - IJMM