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Volumn 5, Issue , 1999, Pages 25-51

Recursion in curve geometry

Author keywords

Curves; Localized induction hierarchy; Solitons

Indexed keywords


EID: 0009021315     PISSN: 10769803     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (37)

References (42)
  • 1
    • 84972511388 scopus 로고
    • The normalized curve shortening flow and homothetic solutions
    • U. Abresch and J. Langer, The normalized curve shortening flow and homothetic solutions, J. Diff. Geom. 23 (1986), 175-196, MR 88d:53001, Zbl 592.53002.
    • (1986) J. Diff. Geom. , vol.23 , pp. 175-196
    • Abresch, U.1    Langer, J.2
  • 2
    • 0001105208 scopus 로고
    • There is more than one way to frame a curve
    • R. Bishop, There is more than one way to frame a curve, Amer. Math. Monthly 82 (1975), 246-251, MR 51 #6604, Zbl 298.53001.
    • (1975) Amer. Math. Monthly , vol.82 , pp. 246-251
    • Bishop, R.1
  • 3
    • 0004478414 scopus 로고
    • A note on a Bäcklund transformation for the continuous Heisenberg model
    • A. Calini, A note on a Bäcklund transformation for the continuous Heisenberg model, Phys. Lett. A 203 (1995), 333-344, MR 96i:82036.
    • (1995) Phys. Lett. A , vol.203 , pp. 333-344
    • Calini, A.1
  • 4
    • 0032359806 scopus 로고    scopus 로고
    • Bäcklund transformations and knots of constant torsion
    • A. Calini and T. Ivey, Bäcklund transformations and knots of constant torsion, J. Knot Theory and its Ramications 7 (1998) 719-746, Zbl 990.04899.
    • (1998) J. Knot Theory and Its Ramications , vol.7 , pp. 719-746
    • Calini, A.1    Ivey, T.2
  • 5
    • 0348077534 scopus 로고    scopus 로고
    • Topology of constant torsion curves evolving under the sine-Gordon equation
    • A. Calini and T. Ivey, Topology of constant torsion curves evolving under the sine-Gordon equation, Phys. Lett. A 254 (1999), 235-243.
    • (1999) Phys. Lett. A , vol.254 , pp. 235-243
    • Calini, A.1    Ivey, T.2
  • 7
    • 0000287170 scopus 로고
    • An elementary geometric characterization of the integrable motions of a curve
    • A. Doliwa and P. Santini, An elementary geometric characterization of the integrable motions of a curve, Phys. Lett. A 185 (1994), 373-384, MR 95b:58075.
    • (1994) Phys. Lett. A , vol.185 , pp. 373-384
    • Doliwa, A.1    Santini, P.2
  • 9
    • 84963023423 scopus 로고
    • The heat equation shrinking convex plane curves
    • M. Gage and R. Hamilton, The heat equation shrinking convex plane curves, J. Diff. Geom. 23 (1986), 69-96, MR 87m:53003, Zbl 621.53001.
    • (1986) J. Diff. Geom. , vol.23 , pp. 69-96
    • Gage, M.1    Hamilton, R.2
  • 10
    • 0041126856 scopus 로고    scopus 로고
    • Taimanov's motion of surfaces and Bäcklund transformations for curves
    • O. Garay and J. Langer, Taimanov's motion of surfaces and Bäcklund transformations for curves, J. Conformal Geometry and Dynamics 3 (1999), 37-49.
    • (1999) J. Conformal Geometry and Dynamics , vol.3 , pp. 37-49
    • Garay, O.1    Langer, J.2
  • 11
    • 0001678450 scopus 로고
    • The Korteweg-de Vries hierarchy as dynamics of closed curves in the plane
    • R. Goldstein and D. Petrich, The Korteweg-de Vries hierarchy as dynamics of closed curves in the plane, Phys. Rev. Lett. 67 (1991), 3203-3206, MR 92g:58050.
    • (1991) Phys. Rev. Lett. , vol.67 , pp. 3203-3206
    • Goldstein, R.1    Petrich, D.2
  • 12
    • 84974277983 scopus 로고
    • A soliton on a vortex filament
    • H. Hasimoto, A soliton on a vortex filament, Journal of Fluid Mechanics 51 (1972), 477-485, Zbl 237.76010.
    • (1972) Journal of Fluid Mechanics , vol.51 , pp. 477-485
    • Hasimoto, H.1
  • 13
    • 3042760691 scopus 로고    scopus 로고
    • Helices, Hasimoto surfaces and Bäcklund transformations
    • to appear
    • T. Ivey, Helices, Hasimoto surfaces and Bäcklund transformations, Canadian Math. Bull., to appear.
    • Canadian Math. Bull.
    • Ivey, T.1
  • 15
    • 4243447316 scopus 로고
    • Solitons and the motion of helical curves
    • G. Lamb, Solitons and the motion of helical curves, Phys. Rev. Lett. 37 (1976), 235-237, MR 57 #13250.
    • (1976) Phys. Rev. Lett. , vol.37 , pp. 235-237
    • Lamb, G.1
  • 16
    • 0347786544 scopus 로고    scopus 로고
    • Straightening soliton curves
    • to appear
    • J. Langer, Straightening soliton curves, Appl. Math. Lett., to appear.
    • Appl. Math. Lett.
    • Langer, J.1
  • 18
    • 0002846809 scopus 로고
    • Poisson geometry of the filament equation
    • J. Langer and R. Perline, Poisson geometry of the filament equation, J. Nonlinear Sci. 1 (1991), 71-93, MR 92k:58118, Zbl 795.35115.
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 71-93
    • Langer, J.1    Perline, R.2
  • 19
    • 36449009745 scopus 로고
    • Local geometric invariants of integrable evolution equations
    • J. Langer and R. Perline, Local geometric invariants of integrable evolution equations, J. Math. Phys. 35 (1994). 1732-1737, MR 95c:58095, Zbl 801.58021.
    • (1994) J. Math. Phys. , vol.35 , pp. 1732-1737
    • Langer, J.1    Perline, R.2
  • 20
    • 0004456299 scopus 로고    scopus 로고
    • Geometric realizations of Fordy-Kulish nonlinear Schrödinger systems
    • to appear
    • J. Langer and R. Perline, Geometric realizations of Fordy-Kulish nonlinear Schrödinger systems, Pac. J. Math., to appear.
    • Pac. J. Math.
    • Langer, J.1    Perline, R.2
  • 21
    • 0041355372 scopus 로고    scopus 로고
    • Curve motion inducing modified Korteweg-de Vries Systems
    • J. Langer and R. Perline, Curve motion inducing modified Korteweg-de Vries Systems, Phys. Lett. A 239 (1998), 36-40.
    • (1998) Phys. Lett. A , vol.239 , pp. 36-40
    • Langer, J.1    Perline, R.2
  • 22
    • 84972507666 scopus 로고
    • The total squared curvature of closed curves
    • J. Langer and D. Singer, The total squared curvature of closed curves, J. Diff. Geom. 20 (1984), 1-22, MR 86i:58030, Zbl 554.53013.
    • (1984) J. Diff. Geom. , vol.20 , pp. 1-22
    • Langer, J.1    Singer, D.2
  • 24
    • 51249166941 scopus 로고
    • Liouville integrability of geometric variational problems
    • J. Langer and D. Singer, Liouville integrability of geometric variational problems, Comment. Math. Helvetici 69 (1994), 272-280, MR 95f:58042, Zbl 819.58017.
    • (1994) Comment. Math. Helvetici , vol.69 , pp. 272-280
    • Langer, J.1    Singer, D.2
  • 25
    • 0030408358 scopus 로고    scopus 로고
    • Lagrangian aspects of the Kirchhoff elastic rod
    • J. Langer and D. Singer, Lagrangian aspects of the Kirchhoff elastic rod, SIAM Review 38 (1996), 605-618, MR 97h:73050, Zbl 859.73040.
    • (1996) SIAM Review , vol.38 , pp. 605-618
    • Langer, J.1    Singer, D.2
  • 27
    • 48749149748 scopus 로고
    • Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids
    • J. Marsden and A. Weinstein, Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids, Phys. D 7 (1983), 305-323, MR 85g:58039, Zbl 576.58008.
    • (1983) Phys. D , vol.7 , pp. 305-323
    • Marsden, J.1    Weinstein, A.2
  • 29
    • 0031499613 scopus 로고    scopus 로고
    • The symmetries of solitons
    • R. Palais, The symmetries of solitons, Bull. Amer. Math. Soc. 34 (1997), 339-403, MR 98f:58111, Zbl 886.58040.
    • (1997) Bull. Amer. Math. Soc. , vol.34 , pp. 339-403
    • Palais, R.1
  • 30
    • 21344490568 scopus 로고
    • Localized induction equation and pseudospherical surfaces
    • R. Perline, Localized induction equation and pseudospherical surfaces, J. Phys. A 27 (1994), 5335-5344, MR 95k:53004, Zbl 843.58070.
    • (1994) J. Phys. A , vol.27 , pp. 5335-5344
    • Perline, R.1
  • 31
    • 0040532859 scopus 로고    scopus 로고
    • Localized induction hierarchy and Weingarten systems
    • R. Perline, Localized induction hierarchy and Weingarten systems, Phys. Lett. A 220 (1996), 70-74, MR 97k:53006.
    • (1996) Phys. Lett. A , vol.220 , pp. 70-74
    • Perline, R.1
  • 32
    • 0000815002 scopus 로고
    • 3
    • 3, Invent. Math. 81 (1985), 379-386, MR 86k:53075, Zbl 585.53051.
    • (1985) Invent. Math. , vol.81 , pp. 379-386
    • Pinkall, U.1
  • 33
    • 0001717693 scopus 로고
    • Rediscovery of the Da Rios equation
    • R. Ricca, Rediscovery of the Da Rios equation, Nature 352 (1991), 561-562.
    • (1991) Nature , vol.352 , pp. 561-562
    • Ricca, R.1
  • 36
    • 0000315041 scopus 로고
    • Soliton surfaces and their applications (soliton geometry from spectral problems)
    • Geometrical Aspects of the Einstein Equations and Integrable Systems (Scheveningen, 1984), Springer-verlag, Berlin
    • A. Sym, Soliton surfaces and their applications (soliton geometry from spectral problems), Geometrical Aspects of the Einstein Equations and Integrable Systems (Scheveningen, 1984), Lecture Notes in Physics, no. 239, Springer-verlag, Berlin, 1985, pp. 154-231, MR 87g:58056, Zbl 583.53017.
    • (1985) Lecture Notes in Physics , vol.239 , pp. 154-231
    • Sym, A.1
  • 37
    • 0001962307 scopus 로고
    • Equilibrium states of elastic rings
    • Tadjbakhsh and Odeh, Equilibrium states of elastic rings, J. Math. Anal. Appl. 18 (1967), 59-74, MR 34 #5355, Zbl 148.19505.
    • (1967) J. Math. Anal. Appl. , vol.18 , pp. 59-74
    • Tadjbakhsh1    Odeh2
  • 39
    • 0000801688 scopus 로고    scopus 로고
    • Surfaces of revolution in terms of solitons
    • I. Taimanov, Surfaces of revolution in terms of solitons, Ann. Global Analysis and Geom. 15 (1997), 419-435, MR 99f:53005, Zbl 896.53007 .
    • (1997) Ann. Global Analysis and Geom. , vol.15 , pp. 419-435
    • Taimanov, I.1
  • 40
    • 0031065010 scopus 로고    scopus 로고
    • Soliton equations and differential geometry
    • Chuu-Lian Terng, Soliton equations and differential geometry, J. Diff. Geom. 45 (1997), 407-445, MR 98e:58102, Zbl 877.53022.
    • (1997) J. Diff. Geom. , vol.45 , pp. 407-445
    • Terng, C.-L.1
  • 41
    • 0001288152 scopus 로고    scopus 로고
    • Robust computation of the rotation minimizing frame for sweep surface modeling
    • W. Wang and B. Joe, Robust computation of the rotation minimizing frame for sweep surface modeling, Computer-Aided Design 29 (1997), 379-391.
    • (1997) Computer-Aided Design , vol.29 , pp. 379-391
    • Wang, W.1    Joe, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.