The geometry of fronts
By Kentaro Saji, Masaaki Umehara, Kotaro Yamada. 2005
218 citations recorded by the source corpus.
We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges. Moreover, it is closely related to the behavior of the Gaussian curvature of a surface near cuspidal edges and swallowtails.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/fa74a63ec80cc54480b78b9b6286f0134af705a5
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Singularities of maximal surfaces (2005, methodology): “As pointed out in [ SUY ], the non-degeneracy of the singular points is also independent of the Riemannian metric g of N3. In fact, Proposition 1.3 in [SUY] can”
- Existence and uniqueness for Legendre curves (2012, unknown): “Let z(γ) be the zigzag number of γ, By the definition of the zigzag number (see [8] for example), z(γ) = |deg([−ν̇(t), γ̇(t)])| = |deg([−`(t), β(t)])| = |deg([− cos θ(t), sin θ(t)])|, where [−ν̇(t), γ̇(t)] is a ratio of two vectors, [−`(t), β(t)] and [− cos θ(t), sin θ(t)] are ratios of two real num”
- Geometric Invariants of Cuspidal Edges (2014, background): “4 Singular Curvature, Normal Curvature, and Umbilic Curvature In this section, we review the singular curvature κs, the limiting normal curvature κn ([15]), and the umbilic curvature κu ([9]).”
- Flat surfaces with singularities in Euclidean 3-space (2006, unknown): “By Corollary 2.11, M 2 can be identified with S 1 × R , and f is constructed from a quadruple ( a ( t ) dt, b ( t ) dt, ˆ ξ ( t ) , ˆ ν ( t )) on S 1 = R / 2 π Z .”