INTEGRABILITY PROPERTY AND GEOMETRIC INTERPRETATION OF CYLINDRICAL EINSTEIN-EQUATION

SHI Jian-Min

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2024年10月30日

Chinese Physics C> 1987, Vol. 11> Issue(2) : 167-174

INTEGRABILITY PROPERTY AND GEOMETRIC INTERPRETATION OF CYLINDRICAL EINSTEIN-EQUATION

SHI Jian-Min ^,

Jiangsu Yangzhou Teachers College

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Abstract：
We discuss cylindrical Einstein-equation via the G-gauge covariant formulation, the basic equations are related to the first and the second fundamental differential forms on the soliton surfaces in the symmetric space. By means of the dual symmetry of the system, the linear scattering equations, Bäcklund transformations and Ricati-equations are established, whose integrabilities are shown. The geometric meanings of Bäcklund transformations and Riccati-equations are obtained.

References

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K. C. Chou, Proc. of the Symposium on Y-M Gauge Theories (Beijing December 1984) Commun. Theot.Phys. Vol. 4 No. 5(1985), 532.[2] M. J. Tblowitz, D. T. Kaup, A. C. Newell, H. Segur, Phys. Rev. Leu., 31(1973), 125; Stud. Appl. Math53(1974), 249.[3] R. Sasaki, Nucl. Phys., 8154(1979), 343.[4] B. Y. Hou, B. Y. Hou, P. Wang, J. Phys. A. Math. Gen., 18(1985), 165.[5] B. Y. Hou, B. Y. Hou. P. Wang, Ins. J. Mod. Phys, 1(1986), 193.[6] B. Y. Hou, B. P. Wang, Proe. of the 3-rd Grassmann Meeting, P. 1033 (Shanghai 1983).[7] D. Maison, J. Math, Phys., Vol. 20 No. 5(1979), 871.[8] K. Pohlmeyer, Cornrntrn. Math. Phys., 46(1976); 207.[9] Y. S. WU, Cotrn. Math. Phys., 90(1983), 461.[10] D. Levi, O. Ragniaw, A. Sym, Lett. AL Nuo. Cim., 33(19821, 401.[11] L. L. Chau, B. Y. Hou, X. C. Song, Phys. Lett., B151(1985), 421.[12] S. S. Chern, C. L. Terng, Rocky Mountain .Jour. of Math., 10(1980); 105.[13] B. Y. Hou, P. Wang, Proc. of the Symposium on Y-M Gauge Theories (Beijing December I984) Commun.Theor. Phys. 4(1985), 729.

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SHI Jian-Min. INTEGRABILITY PROPERTY AND GEOMETRIC INTERPRETATION OF CYLINDRICAL EINSTEIN-EQUATION[J]. Chinese Physics C, 1987, 11(2): 167-174.

SHI Jian-Min. INTEGRABILITY PROPERTY AND GEOMETRIC INTERPRETATION OF CYLINDRICAL EINSTEIN-EQUATION[J]. Chinese Physics C, 1987, 11(2): 167-174. 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

INTEGRABILITY PROPERTY AND GEOMETRIC INTERPRETATION OF CYLINDRICAL EINSTEIN-EQUATION

SHI Jian-Min ^,

Corresponding author: SHI Jian-Min,

Jiangsu Yangzhou Teachers College

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1987-04-05

Abstract: We discuss cylindrical Einstein-equation via the G-gauge covariant formulation, the basic equations are related to the first and the second fundamental differential forms on the soliton surfaces in the symmetric space. By means of the dual symmetry of the system, the linear scattering equations, Bäcklund transformations and Ricati-equations are established, whose integrabilities are shown. The geometric meanings of Bäcklund transformations and Riccati-equations are obtained.