Abstract
In this paper, we study over-determined systems of the following type: F u = α + βe F , F v = γ + δe −F . For a principal curvature function k of a surface in E 3 with no umbilical points and nowhere zero Gaussian curvature, F : = log k 2 is a solution of an over-determined system of the above type on the surface. We will obtain a necessary and sufficient condition of the existence of a solution of an over-determined system of the above type. In particular, we will characterize a semisurface with nowhere zero curvature which can become a surface in E 3. We will present a characterization of a semisurface with nowhere zero curvature such that just two distinct surfaces in E 3, up to a motion of E 3, share the given semisurface structure.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
