Mechanical theorem proving in differential geometry |
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Authors: | Hongbo Li |
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Institution: | (1) Institute of Systems Science, Chinese Academy of Sciences, 100080 Beijing, China |
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Abstract: | An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem
proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chem’s theorems:
“The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces.” Some other theorems
are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks.
Project supported partially by the National Natural Science Foundation of China. |
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Keywords: | Wu’ s method differential forms Chern’ s theorem |
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