THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

WU Yong-Shi; GE Mo-Lin

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2024年10月30日

Chinese Physics C> 1983, Vol. 7> Issue(5) : 560-564

THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

WU Yong-Shi ^, ,
GE Mo-Lin

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Abstract：
The geometric meaning of the Riccati equation related to the structure of space is discussed. It is shown that the Riccati equation satisfied by the stereographic projection is essentially the structure equation of space.

References

[1]

有关Backlund变换的总结见高玲丽, 广州基本粒子物理理论会议文集(1980).变换性质及与手征场的关系见:K. Pohlmeyer, Cmmun. Math. Phys., 96(1976), 207.[2] V. E. Zakharov and A. B. Shabat, JETP 34(1972), 62.[3] R. Sasaki, Nucl. Phys., B154(1979), 343.[4] 侯伯元, 在上海广义相对论精确解讨论班上的报告(1982).[5] L. P. Eisenhart, "A Treatise on the Differential Geometry of Curves and Surfaces" (1949).[6] 葛墨林, 段一士, 高能物理与核物理, 4(1980),173.[7] 侯伯宇、段一士, 葛墨林, 物理学报, 25(1976),519.

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WU Yong-Shi and GE Mo-Lin. THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION[J]. Chinese Physics C, 1983, 7(5): 560-564.

WU Yong-Shi and GE Mo-Lin. THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION[J]. Chinese Physics C, 1983, 7(5): 560-564. shu

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Received: 1900-01-01
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION

WU Yong-Shi ^,
GE Mo-Lin

Corresponding author: WU Yong-Shi,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1983-10-05

Abstract: The geometric meaning of the Riccati equation related to the structure of space is discussed. It is shown that the Riccati equation satisfied by the stereographic projection is essentially the structure equation of space.