Evolutoids and pedaloids of frontals on timelike surfaces

Evolutoids and pedaloids of frontals on timelike surfaces

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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 mezquila brooklyn 3-space.As an application 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 steely dan gaucho t-shirt the pedaloids of frontals and the pedal surfaces of evolutoids.

Finally, we give some examples to demonstrate the results.