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3. Also, using
"... Ristow Montes Abstract. In this paper we establish equations for the Gaussian Curvature and for the Laplacian of a minimal surface in the Heisenberg Group H3. Using GaussCodazzi equations we prove that the contact angle (0 < β < pi2) is constant for compact minimal surfaces in H ..."
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Ristow Montes Abstract. In this paper we establish equations for the Gaussian Curvature and for the Laplacian of a minimal surface in the Heisenberg Group H3. Using GaussCodazzi equations we prove that the contact angle (0 < β < pi2) is constant for compact minimal surfaces in H
APPLICATIONS OF LOOP GROUP FACTORIZATION TO GEOMETRIC SOLITON EQUATIONS
, 2006
"... Abstract. The 1d Schrödinger flow on S 2, the GaussCodazzi equation for flat Lagrangian submanifolds in R 2n, and the spacetime monopole equation are all examples of geometric soliton equations. The linear systems with a spectral parameter (Lax pair) associated to these equations satisfy the real ..."
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Abstract. The 1d Schrödinger flow on S 2, the GaussCodazzi equation for flat Lagrangian submanifolds in R 2n, and the spacetime monopole equation are all examples of geometric soliton equations. The linear systems with a spectral parameter (Lax pair) associated to these equations satisfy
NULL HYPERSURFACES OF FINSLER SPACES
"... ABSTRACT. We construct the null transversal vector bundle of a null hypersurface N in an indefinite Finslet space F n and obtain the induced geometric objects on N and the GaussCodazzi equations of N. 0. Introduction. The theory of Finsler subspaces is one of the most difficult theories in Finsler ..."
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ABSTRACT. We construct the null transversal vector bundle of a null hypersurface N in an indefinite Finslet space F n and obtain the induced geometric objects on N and the GaussCodazzi equations of N. 0. Introduction. The theory of Finsler subspaces is one of the most difficult theories
Stationary VeselovNovikov equation and isothermally asymptotic surfaces in projective differential geometry
, 1998
"... It is demonstrated that the stationary VeselovNovikov (VN) and the stationary modified VeselovNovikov (mVN) equations describe one and the same class of surfaces in projective differential geometry: the socalled isothermally asymptotic surfaces, examples of which include arbitrary quadrics and cu ..."
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and cubics, quartics of Kummer, projective transforms of affine spheres and rotation surfaces. The stationary mVN equation arises in the Wilczynski approach and plays the role of the projective ”GaussCodazzi ” equations, while the stationary VN equation follows from the Lelieuvre representation of surfaces
hep–th/9604195 UNIVERSAL ASPECTS OF STRING PROPAGATION ON CURVED BACKGROUNDS
, 1996
"... String propagation on D–dimensional curved backgrounds with Lorentzian signature is formulated as a geometrical problem of embedding surfaces. When the spatial part of the background corresponds to a general WZW model for a compact group, the classical dynamics of the physical degrees of freedom is ..."
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is governed by the coset conformal field theory SO(D−1)/SO(D−2), which is universal irrespectively of the particular WZW model. The same holds for string propagation on D–dimensional flat space. The integration of the corresponding Gauss–Codazzi equations requires the introduction of (non
CL.: Conformally flat submanifolds in spheres and integrable systems. arXiv:mathdg/0803.2754v2
, 2008
"... ABSTRACT. É. Cartan proved that conformally flat hypersurfaces in Sn+1 for n> 3 have at most two distinct principal curvatures and locally envelop a oneparameter family of (n − 1)spheres. We prove that the GaussCodazzi equation for conformally flat hypersurfaces in S4 is a soliton equation, and ..."
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Cited by 3 (3 self)
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ABSTRACT. É. Cartan proved that conformally flat hypersurfaces in Sn+1 for n> 3 have at most two distinct principal curvatures and locally envelop a oneparameter family of (n − 1)spheres. We prove that the GaussCodazzi equation for conformally flat hypersurfaces in S4 is a soliton equation
TABLEAUX OVER LIE ALGEBRAS, INTEGRABLE SYSTEMS, AND CLASSICAL SURFACE THEORY
, 2006
"... Abstract. Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfa ..."
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Cited by 4 (2 self)
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surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G0system of Terng and the curved flat system of Ferus–Pedit may be obtained as special cases of this construction. Some classes of surfaces in projective differential geometry whose Gauss–Codazzi equations
Surfaces in 3space possessing nontrivial deformations which preserve the shape operator
, 2001
"... The class of surfaces in 3space possessing nontrivial deformations which preserve principal directions and principal curvatures (or, equivalently, the shape operator) was investigated by Finikov and Gambier as far back as in 1933. We review some of the known examples and results, demonstrate the in ..."
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the integrability of the corresponding GaussCodazzi equations and draw parallels between this geometrical problem and the theory of compatible Poisson brackets of hydrodynamic type. It turns out that coordinate hypersurfaces of the northogonal systems arising in the theory of compatible Poisson brackets
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