The geometry of fronts
From MaRDI portal
Publication:2389143
DOI10.4007/annals.2009.169.491zbMath1177.53014arXivmath/0503236OpenAlexW2135257082MaRDI QIDQ2389143
Kentaro Saji, Kotaro Yamada, Masaaki Umehara
Publication date: 14 July 2009
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0503236
Surfaces in Euclidean and related spaces (53A05) Singularities of differentiable mappings in differential topology (57R45) Critical points of functions and mappings on manifolds (58K05)
Related Items (85)
Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint ⋮ Behavior of principal curvatures of frontals near non-front singular points and their applications ⋮ Isometric deformations of cuspidal edges ⋮ Asymptotic behavior of flat surfaces in hyperbolic 3-space ⋮ Legendrian dualities and evolute-involute curve pairs of spacelike fronts in null sphere ⋮ Approximating singularities by a cuspidal-edge on a maxface ⋮ The singular evolutoids set and the extended evolutoids front ⋮ Singularities of Gauss maps of wave fronts with non-degenerate singular points ⋮ Kosambi–Cartan–Chern Analysis of the Nonequilibrium Singular Point in One-Dimensional Elementary Catastrophe ⋮ Complete flat fronts as hypersurfaces in Euclidean space ⋮ On the maximal number of exceptional values of Gauss maps for various classes of surfaces ⋮ On the flat geometry of the cuspidal edge ⋮ Normal form of the swallowtail and its applications ⋮ Surfaces of revolution of frontals in the Euclidean space ⋮ Geometric algebra of singular ruled surfaces ⋮ Existence and uniqueness for Legendre curves ⋮ Gauss maps on canal hypersurfaces of generic curves in \(\mathbb{R}^4\) ⋮ Evolutes of fronts in the Euclidean plane ⋮ Koenderink type theorems for fronts ⋮ Isometric immersions with singularities between space forms of the same positive curvature ⋮ Surfaces of constant curvature in \(\mathbb R^3\) with isolated singularities ⋮ \(\ell\)-convex Legendre curves and geometric inequalities ⋮ The fundamental theorem for singular surfaces with limiting tangent planes ⋮ The Gauss-Bonnet theorem for coherent tangent bundles over surfaces with boundary and its applications ⋮ Geometry of cuspidal edges with boundary ⋮ Axial curvatures for corank 1 singular \(n\)-manifolds in \(\mathbb{R}^{n+k}\) ⋮ Framed surfaces in the Euclidean space ⋮ Singularities of Gauss maps of frontal surfaces with non-front singular points ⋮ Extendibility and boundedness of invariants on singularities of wavefronts ⋮ Focal surfaces of fronts associated to unbounded principal curvatures ⋮ Parallel and dual surfaces of cuspidal edges ⋮ The Gauss-Bonnet type theorem for future directed fronts in hyperbolic 3-space and de Sitter 3-space ⋮ Caustics of pseudo-spherical surfaces in the Euclidean 3-space ⋮ Clifford structures, bilegendrian surfaces, and extrinsic curvature ⋮ Timelike sweeping surfaces and singularities ⋮ Singularities of frontal surfaces ⋮ The duality of conformally flat manifolds ⋮ Singularity properties of Lorentzian Darboux surfaces in Lorentz-Minkowski spacetime ⋮ Cuspidal edges with the same first fundamental forms along a knot ⋮ Value distribution of the Gauss map of improper affine spheres ⋮ On the index of principal foliations of surfaces in R^3 with corank 1 singularities ⋮ Duality on generalized cuspidal edges preserving singular set images and first fundamental forms ⋮ Local differential geometry of cuspidal edge and swallowtail ⋮ Flat fronts in hyperbolic 3-space with prescribed singularities ⋮ GAUSSIAN CURVATURE AND UNICITY PROBLEM OF GAUSS MAPS OF VARIOUS CLASSES OF SURFACES ⋮ Timelike constant mean curvature surfaces with singularities ⋮ Singularities of maximal surfaces ⋮ Value distribution for the Gauss maps of various classes of surfaces ⋮ The geometry of corank 1 surfaces in ℝ4 ⋮ Relating second order geometry of manifolds through projections and normal sections ⋮ Singularities of spacelike constant mean curvature surfaces in Lorentz–Minkowski space ⋮ Geometry of bifurcation sets of generic unfoldings of corank two functions ⋮ Geometry of surfaces in \(\mathbb{R}^5\) through projections and normal sections ⋮ A connection between flat fronts in hyperbolic space and minimal surfaces in Euclidean space ⋮ On Gaussian curvatures and singularities of Gauss maps of cuspidal edges ⋮ The Hawking energy on the past lightcone in cosmology ⋮ Coherent tangent bundles and Gauss-Bonnet formulas for wave fronts ⋮ Criteria for \(D_4\) singularities of wave fronts ⋮ Extrinsic diameter of immersed flat tori in \(S^3\) ⋮ Singularities of Blaschke normal maps of convex surfaces ⋮ The duality between singular points and inflection points on wave fronts ⋮ Singularities of a surface given by Kenmotsu-type formula in Euclidean three-space ⋮ Isometric immersions of \({{\mathbb R}^2}\) into \({{\mathbb R}^4}\) and perturbation of Hopf tori ⋮ On the geometry of folded cuspidal edges ⋮ Intrinsic invariants of cross caps ⋮ On Legendre curves in normed planes ⋮ Isometric deformations of wave fronts at non-degenerate singular points ⋮ A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space ⋮ The dually flat structure for singular models ⋮ Behavior of Gaussian Curvature and Mean Curvature Near Non-degenerate Singular Points on Wave Fronts ⋮ Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds ⋮ Anti-orthotomics of frontals and their applications ⋮ Orientability of linear Weingarten surfaces, spacelike CMC-1 surfaces and maximal surfaces ⋮ Dualities of differential geometric invariants on cuspidal edges on flat fronts in the hyperbolic space and the De Sitter space ⋮ Families of spherical surfaces and harmonic maps ⋮ Semi-discrete maximal surfaces with singularities in Minkowski space ⋮ The space of Lorentzian flat tori in anti-de Sitter $3$-space ⋮ FOCAL SURFACES OF WAVE FRONTS IN THE EUCLIDEAN 3-SPACE ⋮ The axial curvature for corank 1 singular surfaces ⋮ Principal curvatures and parallel surfaces of wave fronts ⋮ Intrinsic properties of surfaces with singularities ⋮ Hyperplane families creating envelopes ⋮ Contact properties of surfaces in \({\mathbb R}^3\) with corank 1 singularities ⋮ Local normal forms of EM-wavefronts in affine flat coordinates ⋮ The sub-parabolic lines in the Minkowski 3-space
This page was built for publication: The geometry of fronts
