Generalizations of Killing vector fields in sol space

We consider two generalizations of the Killing vector fields in the 3D Sol space. Conformal Killing vector fields are the first generalization, 2-Killing vector fields are the second. We characterize proper conformal Killing vector fields and determine some proper 2-Killing vector fields in Sol space.

b-Smarandache tm₂ curves of biharmonic new type b-slant helices according to Bishop frame in the Sol space Sol³

In this paper, we study b-Smarandache tm₂ curves of biharmonic new type b-slant helix in the Sol³. We characterize the b-Smarandache tm₂ curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol³.

Integral equations of biharmonic constant π₁-slope curves according to type-2 Bishop frame in the SOL space

In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.

Parallel surfaces to normal ruled surfaces of general helices in the sol space Sol³

In this paper, parallel surfaces to normal ruled surface of general helices in the Sol³ are studied. Also, explicit parametric equations of parallel surfaces to normal ruled surface of general helices in the Sol³ are found.