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.
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