Pointwise Slant Riemannian Maps (PSRM) to almost hermitian manifolds

The aim of the present paper is to introduce new class of Riemannian maps which are called pointwise slant Riemannian maps (briefly, PSRM) as a natural generalization of pointwise slant submanifolds which were introduced by Chen and Garay (Turkish J Math 36:630–640, 2012) and pointwise slant submersions which were defined by Lee and S¸ahin (Bull Korean Math Soc 51(4):1115–1126, 2014]. We mention many examples and investigate the geometry of foliations which are arisen from the definition of a PSRM and obtain decomposition theorems using the existence of PSRM. Moreover, we find necessary and sufficient conditions for PSRM to be totally geodesic and investigate the harmonicity of such maps. Finally, we get two inequalities in terms of the second fundamental form of a PSRM and check the equality case.