Pointwise slant Riemannian maps from Kaehler manifolds

Abstract

Pointwise slant submanifolds were introduced by Chen and Garay (2012) [16] as a natural generalization of slant submanifolds. On the other hand, pointwise slant submersions were defined by Lee and Şahin (2014) [29] as a natural generalization of slant submersions. In this paper, as a generalization of pointwise slant submanifolds and pointwise slant submersions, we introduce pointwise slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds, present examples and characterizations. We investigate the geometry of foliations which are arisen from the definition of a pointwise slant Riemannian map and obtain decomposition theorems by using the existence of pointwise slant Riemannian maps. We also investigate the harmonicity of such maps and find necessary and sufficient conditions for pointwise slant Riemannian maps to be totally geodesic. Finally, we study some curvature relations in complex space forms, involving Casorati curvatures for pointwise slant Riemannian maps.