Communications of the
Korean Mathematical Society CKMS

In three dimensional Euclidean space we consider kinematical invariants of the surface which is generated by the motion of a planar curve, especially, the surface which is foliated by circles. At first we characterize the properties of single parameter plane with the theories of unit spherical curve in three dimensional Euclidean space. Then using these results we give the invariants and differential invariants, kinematical properties and some special examples of the surface foliated by circles. The methods established here can be used to the other kinds of the surface in three dimensional Euclidean space.

Keywords: Kinematical invariant, circled surface, structure function, differential invariant, ruled surface

MSC numbers: 53A05, 53A55, 53C12, 53A04

Supported by: Seoung Dal Jung Supported by National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2018R1A2B2002046). Huili Liu Partially supported by NSFC; Joint Research of NSFC and NRF; Chern Institute of Mathematics and Northeastern University.