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Painlevé Equations in the Differential Geometry of Surfaces

Medium: Buch
ISBN: 978-3-540-41414-8
Verlag: Springer Berlin Heidelberg
Erscheinungstermin: 12.12.2000
Lieferfrist: bis zu 10 Tage

Since the time of surfaces -+ in differential Gauss, parametrized (x, y) P(x, y) have been described a frame attached to the moving geometry through TI(x, y) surface. One introduces the Gauss- which linear dif- Weingarten equations are, ferential equations = U = TIX T1, VT', !PY (1. for the and their condition frame, compatibility - = V + [U, V] 0, UY (1.2) which the Gauss-Codazzi For surfaces in three-dim- represents equations. a sional Euclidean the frame T1 lies in the usually or space, group SO(3) SU(2). On the other a of a non-linear in the form hand, representation equation (1.2) is the of the of of starting point theory integrable equations (theory solitons), which in mathematical in the 1960's appeared physics [NMPZ, AbS, CD, FT, More the differential for the coefficients of AbC]. exactly, partial equation (1.2) the matrices U and V is considered to be if these matrices can be integrable, extended to U V non-trivially a one-parameter family (x, y, A), (x, y, A) satisfying - = + U(A)y V(A). [U(A), V(A)] 0, (1-3) so that the differential is and original partial equation preserved.'. Usually U(A) V are rational functions of the which is called the (A) parameter A, spectral param- In soliton the eter is called the Lax. theory, representation (1.3) representation the Zakharov-Shabat or representation [ZS].


Produkteigenschaften


  • Artikelnummer: 9783540414148
  • Medium: Buch
  • ISBN: 978-3-540-41414-8
  • Verlag: Springer Berlin Heidelberg
  • Erscheinungstermin: 12.12.2000
  • Sprache(n): Englisch
  • Auflage: 2000
  • Serie: Lecture Notes in Mathematics
  • Produktform: Kartoniert
  • Gewicht: 201 g
  • Seiten: 120
  • Format (B x H x T): 155 x 235 x 8 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

1. Introduction.- 2. Basics on Painlevé Equations and Quaternionic Description of Surfaces.- 3. Bonnet Surfaces in Euclidean Three-space.- 4. Bonnet Surfaces in S3 and H3 and Surfaces with Harmonic Inverse Mean Curvature.- 5. Surfaces with Constant Curvature.- 6. Appendices.