Integrable System and Motion of Curves in Projective and Similarity Geometries |
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| Authors: | HOU Yu-Qing |
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| Affiliation: | Department of Electronics, Northwest University, Xi'an 710069, China |
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| Abstract: | Based on the natural frame in the projective geometry, motions of
curves in projective geometry are studied. It is shown that
several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleration
field and governed by endowing an extra
space variable in similarity geometry P3 is also studied. |
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| Keywords: | motion of curve similarity geometry projective geometry integrable equation |
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