K-type slant helices on spacelike and timelike surfaces

Y We have derived a necessary and sufficient condition for a non-null normal spacelike curve lying in a spacelike or a timelike surface M subset of E-1(3) , so that the curve becomes a K-type spacelike slant helix with K is an element of {1, 2, 3}. We have used Darboux frame to define necessary and sufficient conditions. An example is given for a 1-type spacelike slant helix having a spacelike normal and a timelike binormal.

Automated summary

The study presents a necessary and sufficient condition for a non-null normal spacelike curve to become a K-type spacelike slant helix, utilizing the Darboux frame for definition. An example is provided to demonstrate a 1-type spacelike slant helix with a spacelike normal and a timelike binormal.