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Motion of curves and surfaces in affine geometry |
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| Authors: | Changzheng Qu Shunli Zhang |
| Affiliation: | Department of Mathematics, Northwest University, Xi’an 710069, PR China |
| Abstract: | In this paper, motion of space curves by endowing an extra space variable in centro-affine geometry is discussed. It is shown that the 2 + 1-dimensional integrable shallow water wave equation arises from such motion. Motion of curves specified by acceleration field in centro-affine geometry is also investigated, some integrable system are found to be associated with the curve motion law. |
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