Construction of Surfaces with Constant Mean Curvature Along a Timelike Curve

Abstract

 Surfaces constructed using a given timelike curve  Constraints for surfaces to have constant mean curvature along the given curve are obtained

Surface family interpolating a common spherical indicatrix curve

“…The study of curves and surfaces has wide application areas such as architectural design, computer aided design, astronomy, astrophysics and genetics [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. We encounter curves and surfaces in every differential geometry book.…”

“…Recently, Güler [16] presented the geometric relationship between the focal surfaces and the original surface. Bayram [7] constructed surfaces with constant mean curvature along a timelike curve. Surfaces with a common adjoint curve are obtained in [9].…”

On the Surfaces with Constant Mean Curvature along a Curve in the Lie Group

“…The method used in these publications is as follows: the isoparametric curve's geodesic, asymptotic, and line-of-curvature conditions have been determined, and the parametric surfaces have been created as a linear combination of that curve and its Frenet frame. A new study on construction surfaces with constant curvatures along a particular curve was recently proposed by (Cosanoglu et al 2020;Bayram et al 2022).…”

On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group

“…The process in these papers is as follows: conditions for that curve to be a geodesic, asymptotic, and line of curvature have been given, and the parametric surface has been constructed as a linear combination of an isoparametric curve and its Frenet frame. A new study on construction surfaces with constant curvatures along a given curve was recently proposed by Bayram et al [13,14].…”