Pointwise semi-slant Riemannian {\bf PSSR} maps from almost Hermitian manifolds

Abstract

In this paper, as a generalization of pointwise slant submanifolds [B-Y. Chen and O. J. Garay, {\it  Pointwise slant submanifolds in almost Hermitian manifolds,} Turk J Math 36, (2012), 630-640.], pointwise slant submersions [J.W.Lee and B. \d{S}ahin,  {\it Pointwise slant submersions,}  Bulletin of the Korean Mathematical Sosiety, 51(4), (2014), 115-1126.] and pointwise slant Riemannian maps [Y. G\"{u}nd\"{u}zalp and  M. A. Akyol, {\it Pointwise slant Riemannian maps from Kaehler manifolds}, Journal of Geometry and Physics, 179, (2002), 104589.], we introduce pointwise semi-slant Riemannian maps (briefly, {\bf PSSR} maps) from almost Hermitian manifolds to Riemannian manifolds, present examples and characterizations.  We also investigate the harmonicity of such maps. Moreover, we give Chen-Ricci inequality for a {\bf PSSR} map. Finally, we study some curvature relations in complex space forms, involving Casorati curvatures for {\bf PSSR} maps