Conformal anti-invariant riemannian maps to KÄhler manifolds

Abstract

We introduce conformal anti-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds and show that they include both anti-invariant submanifolds and anti-invariant Riemannian maps. We give non-trivial examples, investigate the geometry of certain distributions and obtain decomposition theorems for the base manifold. The harmonicity and totally geodesicity of conformal anti-invariant Riemannian maps are also obtained. Moreover, we study weakly umbilical conformal Riemannian maps and obtain a classification theorem for umbilical conformal anti-invariant Riemannian maps. © 2018, Politechnica University of Bucharest. All rights reserved.