Abstract
In this paper, a new characterization for darboux curves in Heis₃ is completely given. Then, a new classification for translation surface , which is generated by darboux curve in Heis₃ is obtained.
Highlights
The orthonormal basis for the corresponding Lie algebra: we have with e1
Where the (i, j)−element in the table above equals for ∇ei ej for our basis
If α is a darboux curve on surface M, δ′u1t1
Summary
The left-invariant Lorentzian metric on Heis[3] is g = ds2 = −dx2 + dy2 + (xdy + dz)[2 ]. The orthonormal basis for the corresponding Lie algebra: we have with e1 Where the (i, j)−element in the table above equals for ∇ei ej for our basis Let γ : I −→ Heis[3] be a unit speed spacelike curve with timelike binormal and {T,N,B} are Frenet vector fields, Frenet formulas are as follows
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
