turkmath.org

As a generalization of conformal isometric immersions and conformal Riemannian submersions, conformal Riemannian maps have been studied intensively recently, and the geometric results obtained for conformal isometric immersions and conformal Riemannian submersions have been extented to a broader class. The purpose of this talk is to present recent developments on conformal Riemannian maps to almost Hermitian manifolds. Geometric notions in almost Hermitian manifolds are defined according to the complex structure on the manifolds. Considering this approach, invariant, anti-invariant, semiinvariant and slant classes of conformal Riemann maps are introduced, examples are given for each class, characterizations are obtained and the properties of the map are presented. In addition, results are given on whether the map of these classes is totally geodesic and harmonic. Considering that these presented conformal Riemannian maps are a broad class of almost Hermitian manifolds including holomorphic submanifold, totally real submanifold, CR-submanifold and slant submanifold, these new geometric concepts seem to have the potential to stimulus new research problems in differential geometry.