Cartan's Equivalence Method
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Cartan''s equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism.Although the answer to this particular question was known in dimension 2 to Gauss and in higher dimensions to Christoffel and perhaps Riemann as well, Élie Cartan and his intellectual heirs developed a technique for answering similar questions for radically different geometric structures. (For exam...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Cartan''s equivalence method is a technique in differential geometry for determining whether two geometrical structures are the same up to a diffeomorphism.Although the answer to this particular question was known in dimension 2 to Gauss and in higher dimensions to Christoffel and perhaps Riemann as well, Élie Cartan and his intellectual heirs developed a technique for answering similar questions for radically different geometric structures. (For example see the Cartan-Karlhede algorithm.) Cartan successfully applied his equivalence method to many such structures, including projective structures, CR structures, and complex structures, as well as ostensibly non-geometrical structures such as the equivalence of Lagrangians and ordinary differential equations. (His techniques were later developed more fully by many others, such as D. C. Spencer and Shiing-Shen Chern.)
