On the Use of Hypercomplex Numbers in Certain Problems of the Modular Group
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چکیده
13. The problem of determining all algebraic minimal surfaces was solved analytically by Weierstrass in 1866 (see his collected works, volume 3, pages 39-52). Darboux, in his Théorie générale des surfaces, part 1, No. 221, has shown that such surfaces can always be generated by the translation of an algebraic curve. This shows that the function F(s) used in the formulas of Weierstrass must be algebraic. Professor Hancock proposes as a problem next to be attacked the question of determining all those minimal surfaces which are not themselves algebraic, but contain a sheaf of algebraic curves.
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