• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.757-774
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• 2024

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.