Spacelike surface families interpolating common asymptotic curves in Minkowski 3-space

In this paper, we propose a method for constructing families of spacelike surfaces in Minkowski 3-space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:mspace width="0.3333em"/> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="double-struck">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> that share Bertrand curves as asymptotic curves. By using marching-scale functions, we derive the necessary conditions, provide flexible formulations, and establish a framework for constructing mutual spacelike Bertrand curves. Examples show how different functions generate surfaces interpolating the common asymptotic curves, offering new insights for geometric modeling and ruled surface theory.