The Transition from Three-Dimensional Embedding to Two-Dimensional Euler-Lagrange Deformation Tensor of the Second Kind: Variation of Curvature Measures |
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| Authors: | Erik W Grafarend |
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| Institution: | 1. Geodaetisches Institut, Geschwister-Scholl-Str. 24D, 70174, Stuttgart, Germany
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| Abstract: | Based on the Stein formulation of changes of curvature parameters, we describe the changes of Riemann two-dimensional manifolds of surface geometries. The three-dimensional left and right Euclidean manifolds with the curvature parameters “geodetic curvature, normal curvature, geodetic torsion” characterize the embedding “Riemann to Euclid” or 2d into 3d. The variation in time of the Euler-Lagrange deformation tensor of the second kind, in short “curvature variation” is studied. |
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