2024-03-28T20:47:54Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/699072022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Framed surfaces in the Euclidean spaceFukunaga, TomonoriTakahashi, Masatomo410A 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69907info:doi/10.14943/84247https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69907/1/pre1103.pdfHokkaido University Preprint Series in Mathematics11031262017-06-21engpublisher