Bibliographic Details
| Title: |
Mannheim-d'Ocagne-Koenderink type formulas for asymptotic directions. |
| Authors: |
FUKUI, Toshizumi1, HONDA, Atsufumi2, UMEHARA, Masaaki3 |
| Source: |
Proceedings of the Japan Academy, Series A: Mathematical Sciences. Jun2026, Vol. 102 Issue 6, p29-35. 7p. |
| Subjects: |
Gaussian curvature, Mathematical singularities, Surface geometry, Euclidean metric, Curvature, Mathematical formulas |
| Abstract: |
We consider a surface embedded in the Euclidean 3-space and fix a tangential vector v at a given point p on the surface. We first review the history of the formula obtained by Mannheim, d'Ocagne and Koenderink, which asserts that the Gaussian curvature of the surface at p can be obtained if one knows "the normal curvature at p with respect to v" and "the curvature at p of the contour line Γ of the surface" with respect to the orthogonal projection induced by v. However, this formula breaks down when v is an asymptotic direction. In such cases, we present analogues of the formula that involve an invariant associated with cusp singularities of Γ. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
