Geometry of cuspidal edges with boundary. (English) Zbl 1383.53004
In this note the authors study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behaviour of the boundary in addition to usual differential geometric invariants of cuspidal edges. They construct a normal form. Several geometric invariants on cuspidal edges are defined and studied. All coefficients of the normal form are differential geometric invariants. They give geometric meanings of these invariants. An application of this study is given by considering flat extensions of flat ruled surfaces with boundaries. The authors also give an appendix on curvature and torsion of space curves with singularities.
Reviewer: Corina Mohorianu (Iaşi)
MSC:
| 53A05 | Surfaces in Euclidean and related spaces |
| 58K05 | Critical points of functions and mappings on manifolds |
| 58K50 | Normal forms on manifolds |
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