From Ramond fermions to Lamé equations for orthogonal curvilinear coordinates

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Science BV
Google Scholar
Research Projects
Organizational Units
Journal Issue
We show how Ramond free neutral Fermi fields lead to a Ƭ-function theory of BKP type which describes iso-orthogonal deformations of systems of orthogonal curvilinear coordinates. We also provide a vertex operator representation for the classical Ribaucour transformation.
©1998 Elsevier Science B.V.
Unesco subjects
[1] L. Bianchi, Lezione di Geometria Differenziale, 3- a ed., Zanichelli, Bologna, 1924. [2] G. Darboux, Lec¸ons sur la theorie generale des surfaces IV, Gauthier-Villars, Paris, 1896. Peprinted by Chelsea Publishing Company, New York, 1972. [3] G. Darboux, Lec¸ons sur les systemes orthogonaux et les coordenées curvilignes (deuxieme edition), Gauthier-Villars, Paris, 1910 (the first edition was in 1897) . Reprinted by Éditions Jacques Gabay, Sceaux, 1993. [4] G. Darboux, Ann. L’Ecole Normale 3 (1866) 97. [5] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, Physica D 4 (1982) 343. [6] A. Doliwa, M. Mañas, L. Martínez Alonso, E. Medina, P.M. Santini, Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets, 1998, solv-intr9803015. [7] R. Dijkgraff, E. Verlinde, H. Verlinde, Nucl. Phys. B 352 (1991) 59. [8] B. Dubrovin, Nucl. Phys. B 379 1992 627. [9] L.P. Eisenhart, A Treatise on the Differential Geometry of Curves and Surfaces, Ginn, Co., Boston, 1909. [10] L.P. Eisenhart, Transformations of Surfaces, Princeton University Press, Princeton, 1923. Reprinted by Chelsea Publishing Company, New York, 1962. [11] D.-Th. Egorov, Comp. Rend. Acad. Sci. Paris 131 (1900) 668; 132 (1901) 174. [12] P. Goddard, D. Olive, Int. J. Mod. Phys. 1 (1986) 303. [13] I.M. Krichever, Func. Anal. Appl. 31 (1997) 25. [14] G. Lamé, Lec çons sur la théorie des coordenées curvilignes et leurs diverses applications, Mallet-Bachalier, Paris, 1859. [15] A. Ribaucour, Comp. Rend. Acad. Sci. Paris 74 (1872) 1489. [16] G. Segal, G. Wilson, Publ. Math. IHES 61 (1985) 5. [17] E. Witten, Nucl. Phys. B 340 (1990) 281. [18] V.E. Zakharov, On Integrability of the Equations Describing N-Orthogonal Curvilinear Coordinate Systems and Hamiltonian Integrable Systems of Hydrodynamic Type I: Integration of the Lame Equations, Preprint, 1996.