Evolutoids and pedaloids of frontals on timelike surfaces

Evolutoids and pedaloids of frontals on timelike surfaces

Blog Article

In this article, we define evolutoids and pedaloids of frontals on timelike surfaces in Minkowski 3-space.The evolutoids of frontals on timelike surfaces are not only the generalization of evolutoids of curves in the Minkowski plane but also the generalization of caustics in Minkowski 3-space.As an application Facial Cleansers of the singularity theory, we classify the singularities of evolutoids and reveal the relationships between the singularities and geometric invariants of frontals.Furthermore, we find that there exists a close connection between the pedaloids of frontals and the pedal surfaces of evolutoids.

Finally, we give MAG CHLORIDE LIQUID some examples to demonstrate the results.