Conformal anti-invariant ${\xi }^{\perp }-$submersions

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.

21 pages. arXiv admin note: substantial text overlap with arXiv:1504.05757, arXiv:1505.07317; text overlap with arXiv:1504.04180, arXiv:1311.1676 by other authors