Framed Surfaces in the Euclidean Space

A framed surface is a smooth surface in the Euclidean space with a moving frame. The framed surfaces may have singularities. We treat smooth surfaces with singular points, that is, singular surfaces more directly. By using the moving frame, the basic invariants and curvatures of the framed surface a...

Full description

Saved in:
Bibliographic Details
Published inBoletim da Sociedade Brasileira de Matemática Vol. 50; no. 1; pp. 37 - 65
Main Authors Fukunaga, Tomonori, Takahashi, Masatomo
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 12.03.2019
Springer Nature B.V
Subjects
Curvature
Euclidean geometry
Euclidean space
Invariants
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Singularity (mathematics)
Theoretical
57R45
Framed surface
Singular point
Frontal
58K05
53A05
Basic invariant
Curvature
Online AccessGet full text

Cover

More Information
Summary:A framed surface is a smooth surface in the Euclidean space with a moving frame. The framed surfaces may have singularities. We treat smooth surfaces with singular points, that is, singular surfaces more directly. By using the moving frame, the basic invariants and curvatures of the framed surface are introduced. Then we show that the existence and uniqueness for the basic invariants of the framed surfaces. We give properties of framed surfaces and typical examples. Moreover, we construct framed surfaces as one-parameter families of Legendre curves along framed curves. We give a criteria for singularities of framed surfaces by using the curvature of Legendre curves and framed curves.
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-018-0090-z