Normal-Like Curves According to the ED-Frame in E41

doi:10.13438/j.cnki.jdzk.2025.03.004

Abstract

Abstract: Based on the extended Darboux (ED)-framework,the normal-like curves under a specific ED-frame in E4 is defined.The concept of normal curves is extended to E41,and the characteristics of normal-like curves are analyzed in depth.Three equations relating the curvature of normal curves on hypersurfaces M are derived.These equations serve as the necessary and sufficient conditions for normal-like curves in E41.By applying the ED-frame,we define the E-expressions in E41 and give concrete application examples.

Key words: normal-like curve, extended Darboux framework, curvature, torsion

HU Na, LIU Haoran. Normal-Like Curves According to the ED-Frame in E41[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(3): 21-29.

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