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Funktsional. Anal. i Prilozhen., 1997, Volume 31, Issue 1, Pages 32–50 (Mi faa444)  

This article is cited in 41 scientific papers (total in 41 papers)

Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations

I. M. Kricheverab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Columbia University


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English version:
Functional Analysis and Its Applications, 1997, 31:1, 25–39

Bibliographic databases:

UDC: 517.9
Received: 23.12.1996

Citation: I. M. Krichever, “Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations”, Funktsional. Anal. i Prilozhen., 31:1 (1997), 32–50; Funct. Anal. Appl., 31:1 (1997), 25–39

Citation in format AMSBIB
\by I.~M.~Krichever
\paper Algebraic-Geometric $n$-Orthogonal Curvilinear Coordinate Systems and Solutions of the Associativity Equations
\jour Funktsional. Anal. i Prilozhen.
\yr 1997
\vol 31
\issue 1
\pages 32--50
\jour Funct. Anal. Appl.
\yr 1997
\vol 31
\issue 1
\pages 25--39

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    2. A. A. Akhmetshin, Yu. S. Vol'vovskii, I. M. Krichever, “Discrete Analogs of the Darboux–Egorov Metrics”, Proc. Steklov Inst. Math., 225 (1999), 16–39  mathnet  mathscinet  zmath
    3. Krichever, I, “Periodic and almost-periodic potentials in inverse problems”, Inverse Problems, 15:6 (1999), R117  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. van de Leur, JW, “The construction of Frobenius manifolds from KP tau-functions”, Communications in Mathematical Physics, 205:3 (1999), 587  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    6. Manas, M, “Dressing methods for geometric nets: II. Orthogonal and Egorov nets”, Journal of Physics A-Mathematical and General, 33:40 (2000), 7181  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. van de Leur, J, “Twisted GL(n) loop group orbit and solutions of the WDVV equations”, International Mathematics Research Notices, 2001, no. 11, 551  mathscinet  isi
    8. O. I. Mokhov, “Integrability of the Equations for Nonsingular Pairs of Compatible Flat Metrics”, Theoret. and Math. Phys., 130:2 (2002), 198–212  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. O. I. Mokhov, “Compatible Metrics of Constant Riemannian Curvature: Local Geometry, Nonlinear Equations, and Integrability”, Funct. Anal. Appl., 36:3 (2002), 196–204  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Bobenko, AI, “Discrete and smooth orthogonal systems: C-infinity-approximation”, International Mathematics Research Notices, 2003, no. 45, 2415  crossref  mathscinet  zmath  isi
    11. Aratyn, H, “Solutions of the WDVV equations and integrable hierarchies of KP type”, Communications in Mathematical Physics, 239:1–2 (2003), 155  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Chekhov, L, “DV and WDVV”, Physics Letters B, 562:3–4 (2003), 323  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Yu. A. Aminov, “Families of submanifolds of constant negative curvature of many-dimensional Euclidean space”, Sb. Math., 197:2 (2006), 139–152  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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    15. Burstall, FE, “The Ribaucour transformation in Lie sphere geometry”, Differential Geometry and Its Applications, 24:5 (2006), 503  crossref  mathscinet  zmath  isi  scopus
    16. A. I. Bobenko, Yu. B. Suris, “On organizing principles of discrete differential geometry. Geometry of spheres”, Russian Math. Surveys, 62:1 (2007), 1–43  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, Theoret. and Math. Phys., 150:2 (2007), 225–243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    20. Bazhanov, VV, “Quantum geometry of three-dimensional lattices”, Journal of Statistical Mechanics-Theory and Experiment, 2008, P07004  crossref  mathscinet  isi  scopus
    21. Bazhanov V.V., Mangazeev V.V., Sergeev S.M., “Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation”, Xvith International Congress on Mathematical Physics, 2010, 23–44  crossref  mathscinet  zmath  isi  scopus
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    23. I. P. Rybnikov, “Minimal Lagrangian submanifolds in $\mathbb C\mathrm P^n$ with diagonal metric”, Siberian Math. J., 52:1 (2011), 105–112  mathnet  crossref  mathscinet  isi
    24. D. A. Berdinskii, I. P. Rybnikov, “On orthogonal curvilinear coordinate systems in constant curvature spaces”, Siberian Math. J., 52:3 (2011), 394–401  mathnet  crossref  mathscinet  isi
    25. E. I. Shamaev, “O reshetkakh Darbu–Egorova v ${\mathbb R}^n$”, Sib. elektron. matem. izv., 10 (2013), 113–122  mathnet
    26. Shemyakova E., “A Package to Work with Linear Partial Differential Operators”, Program. Comput. Softw., 39:4 (2013), 212–219  crossref  mathscinet  zmath  isi  elib  scopus
    27. Shemyakova E., “Proof of the Completeness of Darboux Wronskian Formulae for Order Two”, Can. J. Math.-J. Can. Math., 65:3 (2013), 655–674  crossref  mathscinet  zmath  isi  scopus
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    31. O. A. Bogoyavlenskaya, “Ob odnom klasse konechnozonnykh krivolineinykh ortogonalnykh koordinat”, Sib. elektron. matem. izv., 12 (2015), 947–954  mathnet  crossref
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    33. E. I. Shamaev, “O diskretizatsii parabolicheskikh koordinat”, Sib. elektron. matem. izv., 13 (2016), 1159–1169  mathnet  crossref
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    35. O. I. Mokhov, “O metrikakh diagonalnoi krivizny”, Fundament. i prikl. matem., 21:6 (2016), 171–182  mathnet
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    38. Bobenko I A., Tsarev S., “The Curvature Line Parametrization From Circular Nets on a Surface”, J. Math. Phys., 59:9, SI (2018), 091410  crossref  mathscinet  zmath  isi  scopus
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    41. Dunin-Barkowski P., Norbury P., Orantin N., Popolitov A., Shadrin S., “Primary Invariants of Hurwitz Frobenius Manifolds”, Topological Recursion and Its Influence in Analysis, Geometry, and Topology, Proceedings of Symposia in Pure Mathematics, 100, eds. Liu C., Mulase M., Amer Mathematical Soc, 2018, 297–331  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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