Survey of several kinds of curves and their properties and relations
Presenter Status
Yun Oh, Department of Mathematics
Second Presenter Status
Alexander Navarro, Department of Mathematics
Preferred Session
Poster Session
Start Date
20-10-2023 2:00 PM
End Date
20-10-2023 3:00 PM
Presentation Abstract
Many geometers have investigated space curves using their curvature and torsion. In 1802, Lancret proved that a unit speed curve with nonzero curvature is a (general) helix if and only if there exists a constant c such that $\tau=c\kappa$. Also it is known that a unit speed curve is a rectifying curve if and only if the ratio of the torsion to the curvature is a linear function in terms of the arc-length parameter. This idea of rectifying curves has been generalized to rectifying submanifolds. In this project, we will survey several kinds of space curves and their properties and relations and possibly find a way to generalize to the higher dimensional submanifolds.
Survey of several kinds of curves and their properties and relations
Many geometers have investigated space curves using their curvature and torsion. In 1802, Lancret proved that a unit speed curve with nonzero curvature is a (general) helix if and only if there exists a constant c such that $\tau=c\kappa$. Also it is known that a unit speed curve is a rectifying curve if and only if the ratio of the torsion to the curvature is a linear function in terms of the arc-length parameter. This idea of rectifying curves has been generalized to rectifying submanifolds. In this project, we will survey several kinds of space curves and their properties and relations and possibly find a way to generalize to the higher dimensional submanifolds.