Conformal quasi-bi-slant Riemannian maps

Volume 28, Issue 4, pp 335--349 http://dx.doi.org/10.22436/jmcs.028.04.03

Publication Date: July 11, 2022 Submission Date: January 25, 2022 Revision Date: February 21, 2022 Accteptance Date: May 25, 2022

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Authors

S. Kumar - Shri Jai Narain Post Graduate College, Lucknow, India. S. Kumar - Dr. S. K. S. Women's College Motihari, B. R. Ambedkar Bihar University, India. D. Kumar - T. P. Varma College Narkatiyaganj, B. R. Ambedkar Bihar University, India.

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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Keywords

• Almost Hermitian manifolds
• Riemannian maps
• conformal quasi bi-slant Riemannian maps

MSC

•  53A43
•  53C15
•  53C55

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