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Volumn 24, Issue 5, 2006, Pages 503-520

The Ribaucour transformation in Lie sphere geometry

Author keywords

Bianchi permutability; Legendre map; Lie geometry; Ribaucour transformation; Submanifold

Indexed keywords


EID: 33747366692     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.difgeo.2006.04.007     Document Type: Article
Times cited : (19)

References (28)
  • 1
    • 4243206697 scopus 로고
    • Om ytor med konstant negativ krökning
    • Bäcklund A.V. Om ytor med konstant negativ krökning. Lund Arsskrift 19 (1883)
    • (1883) Lund Arsskrift , vol.19
    • Bäcklund, A.V.1
  • 2
    • 0002111159 scopus 로고
    • Ricerche sulle superficie isoterme e sulla deformazione delle quadriche
    • Bianchi L. Ricerche sulle superficie isoterme e sulla deformazione delle quadriche. Ann. di Mat. 11 (1905) 93-157
    • (1905) Ann. di Mat. , vol.11 , pp. 93-157
    • Bianchi, L.1
  • 4
    • 0003763761 scopus 로고
    • Vorlesungen über Differentialgeometrie III: Differenzialgeometrie der Kreise und Kugeln
    • Springer-Verlag, Berlin
    • Blaschke W. Vorlesungen über Differentialgeometrie III: Differenzialgeometrie der Kreise und Kugeln. Grundlehren der Mathematik vol. 29 (1929), Springer-Verlag, Berlin
    • (1929) Grundlehren der Mathematik , vol.29
    • Blaschke, W.1
  • 7
  • 10
    • 33747352801 scopus 로고    scopus 로고
    • F.E. Burstall, D. Calderbank, Conformal submanifold geometry, in preparation
  • 12
    • 0036638255 scopus 로고    scopus 로고
    • An extension of the classical Ribaucour transformation
    • Dajczer M., and Tojeiro R. An extension of the classical Ribaucour transformation. Proc. London Math. Soc. 85 (2002) 211-232
    • (2002) Proc. London Math. Soc. , vol.85 , pp. 211-232
    • Dajczer, M.1    Tojeiro, R.2
  • 13
    • 12344321056 scopus 로고    scopus 로고
    • Commuting Codazzi tensors and the Ribaucour transformation for submanifolds
    • Dajczer M., and Tojeiro R. Commuting Codazzi tensors and the Ribaucour transformation for submanifolds. Result. Math. 44 (2003) 258-278
    • (2003) Result. Math. , vol.44 , pp. 258-278
    • Dajczer, M.1    Tojeiro, R.2
  • 15
    • 33747345445 scopus 로고
    • Sur certains couples de systèmes triple-orthogonaux
    • Demoulin A. Sur certains couples de systèmes triple-orthogonaux. C. R. Acad. Sci. Paris Sér. I Math. 151 (1910) 796-800
    • (1910) C. R. Acad. Sci. Paris Sér. I Math. , vol.151 , pp. 796-800
    • Demoulin, A.1
  • 17
    • 0003024768 scopus 로고    scopus 로고
    • over(∂, ̄)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice
    • Doliwa A., Manakov S., and Santini P.M. over(∂, ̄)-reductions of the multidimensional quadrilateral lattice. The multidimensional circular lattice. Commun. Math. Phys. 196 (1998) 1-18
    • (1998) Commun. Math. Phys. , vol.196 , pp. 1-18
    • Doliwa, A.1    Manakov, S.2    Santini, P.M.3
  • 18
    • 0002800572 scopus 로고    scopus 로고
    • Geometry of discrete curves and lattices and integrable difference equations
    • Discrete Integrable Geometry and Physics. Vienna, 1996, Oxford University Press, New York
    • Doliwa A., and Santini P.M. Geometry of discrete curves and lattices and integrable difference equations. Discrete Integrable Geometry and Physics. Vienna, 1996. Oxford Lecture Ser. Math. Appl. vol. 16 (1999), Oxford University Press, New York 139-154
    • (1999) Oxford Lecture Ser. Math. Appl. , vol.16 , pp. 139-154
    • Doliwa, A.1    Santini, P.M.2
  • 20
    • 27544433916 scopus 로고    scopus 로고
    • An algebraic superposition formula and the completeness of Bäcklund transformations of (2 + 1)-dimensional integrable systems
    • Translation in:
    • Ganzha E., and Tsarev S. An algebraic superposition formula and the completeness of Bäcklund transformations of (2 + 1)-dimensional integrable systems. Uspekhi Mat. Nauk 51 (1996) 197-198 Translation in:
    • (1996) Uspekhi Mat. Nauk , vol.51 , pp. 197-198
    • Ganzha, E.1    Tsarev, S.2
  • 21
    • 0030327959 scopus 로고    scopus 로고
    • An algebraic superposition formula and the completeness of Bäcklund transformations of (2 + 1)-dimensional integrable systems
    • Ganzha E., and Tsarev S. An algebraic superposition formula and the completeness of Bäcklund transformations of (2 + 1)-dimensional integrable systems. Russian Math. Surveys 51 (1996) 1200-1202
    • (1996) Russian Math. Surveys , vol.51 , pp. 1200-1202
    • Ganzha, E.1    Tsarev, S.2
  • 22
    • 12844283349 scopus 로고    scopus 로고
    • Introduction to Möbius Differential Geometry
    • Cambridge University Press, Cambridge
    • Hertrich-Jeromin U. Introduction to Möbius Differential Geometry. London Mathematical Society Lecture Note Series vol. 300 (2003), Cambridge University Press, Cambridge
    • (2003) London Mathematical Society Lecture Note Series , vol.300
    • Hertrich-Jeromin, U.1
  • 23
    • 33746456381 scopus 로고    scopus 로고
    • Three-dimensional integrable lattices in Euclidean spaces, conjugacy and orthogonality
    • Konopelchenko B., and Schief W. Three-dimensional integrable lattices in Euclidean spaces, conjugacy and orthogonality. Proc. Roy. Soc. London Ser. A 454 (1998) 3075-3104
    • (1998) Proc. Roy. Soc. London Ser. A , vol.454 , pp. 3075-3104
    • Konopelchenko, B.1    Schief, W.2
  • 24
    • 0038439840 scopus 로고    scopus 로고
    • Algebraic-geometrical n-orthogonal curvilinear systems and solutions to the associativity equations
    • Krichever I. Algebraic-geometrical n-orthogonal curvilinear systems and solutions to the associativity equations. Funktsional. Anal. i Prilozhen. 31 (1997) 32-50
    • (1997) Funktsional. Anal. i Prilozhen. , vol.31 , pp. 32-50
    • Krichever, I.1
  • 25
    • 33747363211 scopus 로고    scopus 로고
    • U. Pinkall, Dupin'sche Hyperflächen, PhD thesis, Universität Freiburg, 1981
  • 26
    • 0038785835 scopus 로고    scopus 로고
    • Isothermic surfaces in spaces of arbitrary dimension: integrability, discretization, and Bäcklund transformations-a discrete Calapso equation
    • Schief W.K. Isothermic surfaces in spaces of arbitrary dimension: integrability, discretization, and Bäcklund transformations-a discrete Calapso equation. Stud. Appl. Math. 106 (2001) 85-137
    • (2001) Stud. Appl. Math. , vol.106 , pp. 85-137
    • Schief, W.K.1
  • 27
    • 11244283264 scopus 로고    scopus 로고
    • On Ribaucour transformations and applications to linear Weingarten surfaces
    • Tenenblat K. On Ribaucour transformations and applications to linear Weingarten surfaces. An. Acad. Brasil. Ciênc. 74 (2002) 559-575
    • (2002) An. Acad. Brasil. Ciênc. , vol.74 , pp. 559-575
    • Tenenblat, K.1
  • 28
    • 0003022531 scopus 로고    scopus 로고
    • Description of the n-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. Part I, Integration of the Lamé equations
    • Zakharov V. Description of the n-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type. Part I, Integration of the Lamé equations. Duke Math. J. 94 (1998) 103-139
    • (1998) Duke Math. J. , vol.94 , pp. 103-139
    • Zakharov, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.