Mehmet Akif Akyol

Conformal semi-invariant submersions

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a conformal submersion and show that there are certain product structures on the total space of a conformal semi-invariant submersion. Moreover, we also check the harmonicity of such submersions and find necessary and sufficient conditions of a conformal semi-invariant submersion to be totally geodesic.

Conformal semi-slant submersions

Park and Prasad [Semi-slant submersions, Bull. Korean Math. Soc. 50(3) (2013) 951–962.] defined and studied semi-slant submersions as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions. As a generalization of semi-slant submersions, we introduce conformal semi-slant submersions and study the new submersions from almost Hermitian manifolds onto Riemannian manifolds. We study the integrability of ditributions and the geometry of leaves of a conformal submersion. Moreover, we show that there are certain product structures on base manifold of a conformal semi-slant submersion. We also obtain totally geodesic conditions for such maps. Finally, we give lots of examples.

Semi-invariant ξ⊥-Riemannian submersions from almost contact metric manifolds

As a generalization of anti-invariant ξ⊥-Riemannian submersions, we introduce semi-invariant ξ⊥-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We give examples, investigating the geometry of foliations which arise from the definition of a Riemannian submersion and proving a necessary and sufficient condition for a semi-invariant ξ⊥-Riemannian submersion to be totally geodesic. Moreover, we study semi-invariant ξ⊥-Riemannian submersions with totally umbilical fibers.

Conformal slant submersions from cosymplectic manifolds

Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field

Biharmonic Riemannian submersions

\xi

On Semi-Slant \({\varvec{\xi ^\perp }}\)-Riemannian Submersions

is a vertical vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions and conformal anti-invariant submersions. More precisely, we mention lots of examples and obtain the geometries of the leaves of

Conformal anti-invariant submersions from almost Hermitian manifolds

\ker\pi_{*}

Conformal anti-invariant submersions from cosymplectic manifolds

and

Golden maps between Golden Riemannian manifolds and constancy of certain maps

(\ker\pi_{*})^\perp,

Conformal slant submersions

including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we consider a decomposition theorem on total space of the new submersion.