Simultaneous Developability of Partner Ruled Surfaces according to Darboux Frame in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msup> <a:mrow> <a:mi>E</a:mi> </a:mrow> <a:mrow> <a:mn>3</a:mn> </a:mrow> </a:msup> </a:math>

In this paper, we introduce original definitions of Partner ruled surfaces according to the Darboux frame of a curve lying on an arbitrary regular surface in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:msup> <a:mrow> <a:mi>E</a:mi> </a:mrow> <a:mrow> <a:mn>3</a:mn> </a:mrow> </a:msup> </a:math> . It concerns <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"> <c:mi>T</c:mi> <c:mi>g</c:mi> </c:math> Partner ruled surfaces, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M4"> <e:mi>T</e:mi> <e:mi>n</e:mi> </e:math> Partner ruled surfaces, and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M5"> <g:mi>g</g:mi> <g:mi>n</g:mi> </g:math> Partner ruled surfaces. We aim to study the simultaneous developability conditions of each couple of two Partner ruled surfaces. Finally, we give an illustrative example for our study.