Conformal anti-invariant $ξ^\perp-$submersions

Published 17 Jan 2017 in math.DG | (1701.05117v1)

Abstract: As a generalization of anti-invariant $\xi^{\perp-$Riemannian} submersions, we introduce conformal anti-invariant $\xi^{\perp-$submersions} from almost contact metric manifolds onto Riemannian manifolds. We investigate the geometry of foliations which are arisen from the definition of a conformal submersion and find necessary and sufficient conditions for a conformal anti-invariant $\xi^{\perp-$submersion} to be totally geodesic and harmonic, respectively. Moreover, we show that there are certain product structures on the total space of a conformal anti-invariant $\xi^{\perp-$submersion.}