Stationary Veselov-Novikov equation and isothermally asymptotic surfaces in projective differential geometry
✍ Scribed by E.V. Ferapontov
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 764 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0926-2245
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✦ Synopsis
It is demonstrated that the stationary Veselo-Novikob (VN) and the stationary modified Ve4o\ Novikov (mVN) equations describe one and the same class of surfaces in projective differential geometry: the so-called isothermally asymptotic surfaces. examples of which include arbitrary quadrics and cuhicy. quarticr of Kummer. projective transforms of aftine spheres and rotation surfaces. The stationary mVN equation arises in the Wilczynski approach and plays the role of the projective "Gauss-CodaLzi" equation. while the a,tationary VN equation follows from the Lelieuvre representation of surfaces in 3-space. Thib implies an explicit BLicklund transformation between the stationary VN and mVN equations which i\ an an:tlog of the Miura transformation between their (I + I )-dimensional limits.