Conformal quasi-bi-slant Riemannian maps

Abstract

Conformal maps or horizontally conformal maps are very useful for characterization of harmonic morphisms. Nowadays, many medical problems (directly or indirectly) such as brain imaging (brain surface mapping, [Y. L. Wang, L. M. Lui, X. F. Gu, K. M. Hayashi, T. F. Chan, A. W. Toga, P. M. Thompson, S.-T. Yau, IEEE Transactions on Medical Imaging, \(\bf 26\) (2007), 853--865], [Y. L. Wang, X. F. Gu, K. M. Hayashi, T. F. Chan, P. M. Thompson , S.-T. Yau, Tenth IEEE International Conference on Computer Vision (ICCV'05), \(\bf 2005\) (2005), 1061--1066]) computer graphics ([X. F. Gu, Y. L. Wang, T. F. Chan, P. M. Thompson, S.-T. Yau, IEEE Transactions on Medical Imaging, \(\bf 23\) (2004), 949--958]) etc. can be solved using conformal Riemannian maps. In this paper, as a generalization of conformal Riemannian maps and conformal bi-slant submersions, we introduce conformal quasi-bi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We study the geometry of leaves of distributions which are involved in the definition of the conformal quasi bi-slant Riemannian maps. We work out conditions for such maps to be integrable, totally geodesic and pluriharmonic. We present two examples for the introduced notion.