Article
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Normal Calculus on Moving Surfaces
Version 1
: Received: 6 June 2018 / Approved: 11 June 2018 / Online: 11 June 2018 (09:54:25 CEST)
How to cite: Afas, K.C. Normal Calculus on Moving Surfaces. Preprints 2018, 2018060148. https://doi.org/10.20944/preprints201806.0148.v1 Afas, K.C. Normal Calculus on Moving Surfaces. Preprints 2018, 2018060148. https://doi.org/10.20944/preprints201806.0148.v1
Abstract
This paper presents an extension for principles of Differential Geometry on Surfaces (re-hashed through the budding field of CMS, the Calculus of Moving Surfaces). It analyzes mostly 2D Hypersurfaces with Riemannian Geometry and proposes the construction of a 3D Static Frame combining the Surface Basis Vectors with the Orthogonal Normal Field as a 3D Orthogonal Vector Frame. The paper introduces conventions for manipulating Tensors defined using this 3D Orthogonal Vector Frame as well as Curvature Connections associated with this Vector Frame. It then finally introduces Symbols and Tensors to describe Inner Products and Variance within the 3D Vector Frame and then extends all the above concepts to a surface which is Dynamic utilizing principles from CMS. This formulation has potential to extend identities and concepts from CMS and from Differential Geometry in a compact Tensorial Framework, which agrees with the new Framework proposed by CMS.
Keywords
calculus of moving surfaces; CMS; differential geometry; normal; tensor; hypersurfaces; dynamic
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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