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<p>Julius Weingarten (1836–1910) made significant contributions to differential geometry, particularly in addressing the second problem of applicability. This paper examines his results on this theme, including the introduction of <i>W</i>-surfaces, his research of complete classes of applicable surfaces in the 1980s and the 1890s, and his award-winning 1894 memoir recognised by the Académie des Sciences de Paris. Besides showing how these achievements marked two important stages in Weingarten’s career, by analysing both his publications and correspondence with Luigi Bianchi the paper reconstructs Weingarten’s evolving methods and situates his work within the broader nineteenth-century pursuit of explicit solutions to differential equations.</p>

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The research of Julius Weingarten on the second problem of applicability

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • Rachele Rivis

摘要

Julius Weingarten (1836–1910) made significant contributions to differential geometry, particularly in addressing the second problem of applicability. This paper examines his results on this theme, including the introduction of W-surfaces, his research of complete classes of applicable surfaces in the 1980s and the 1890s, and his award-winning 1894 memoir recognised by the Académie des Sciences de Paris. Besides showing how these achievements marked two important stages in Weingarten’s career, by analysing both his publications and correspondence with Luigi Bianchi the paper reconstructs Weingarten’s evolving methods and situates his work within the broader nineteenth-century pursuit of explicit solutions to differential equations.