Helicoidal Surfaces with Prescribed Curvatures in Some Conformally Flat Pseudo-Spaces of Dimensional Three

Authors : Büşra SANCI, Fırat YERLİKAYA

Pages : 157-169

Doi:10.33401/fujma.1315178

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Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :In this work, we consider the problem of finding explicit parametrizations for non-degenerate helicoidal surfaces with prescribed curvatures in some conformally flat pseudo-spaces with conformal pseudo-metrics whose conformal factors are related to three types of generic cylindrical functions. In the first two, we get a two-parameter family of these surfaces with prescribed extrinsic curvature or mean curvature given by smooth functions. In the last one, we discover a one-parameter family when both curvatures of these surfaces are zero; however, we find a two-parameter family when either one of those curvatures is zero. Also, we support them with examples.
Keywords : Helicoidal surface, extrinsic curvature, conformally flat pseudo space, conformally flat pseudo metric