Framed Surfaces in the Euclidean Space
| Autor: | Masatomo Takahashi, Tomonori Fukunaga |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Surface (mathematics)
Euclidean space General Mathematics basic invariant 010102 general mathematics Mathematical analysis 0102 computer and information sciences Curvature 01 natural sciences frontal Manifold framed surface Global analysis 010201 computation theory & mathematics Moving frame curvature Gravitational singularity 0101 mathematics singular point Legendre polynomials Mathematics |
| Zdroj: | Bulletin of the Brazilian Mathematical Society, New Series. 50:37-65 |
| ISSN: | 1678-7544 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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