Translationsfl�chen in der �quiaffinen Differentialgeometrie

Pabel, Helmut

doi:10.1007/bf01225881

Cited by 7 publications

(6 citation statements)

References 6 publications

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“…This class of surfaces has been studied previously by Pabel [15], Binder [1], Magid and Vrancken [14], and other geometers. All classes mentioned are very rich.…”

Section: Introductionmentioning

confidence: 94%

Linear Weingarten centroaffine translation surfaces in R3

Yang

Liu

2011

Journal of Mathematical Analysis and Applications

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“…This class of surfaces has been studied previously by Pabel [15], Binder [1], Magid and Vrancken [14], and other geometers. All classes mentioned are very rich.…”

Section: Introductionmentioning

confidence: 94%

Linear Weingarten centroaffine translation surfaces in R3

Yang

Liu

2011

Journal of Mathematical Analysis and Applications

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“…This class of surfaces has been studied previously by Pabel [15], Binder [1], Magid and Vrancken [14], and other geometers. Pabel has discussed translation surfaces with equiaffine methods in affine 3-space R 3 .…”

Section: Introductionmentioning

confidence: 99%

Centroaffine Translation Surfaces in $${\mathbb{R}}^3$$

Yang

Liu

2009

Results. Math.

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The centroaffine theorema egregium χ = J − n n−1 G(T, T ) + 1 is a fundamental scalar identity in the centroaffine differential geometry for nondegenerate hypersurface immersions. Here n is the dimension of the hypersurface, χ the normalized scalar curvature of the centroaffine metric G, J the Pick invariant and T the centroaffine Tchebychev vector field. In this paper we study non-degenerate centroaffine translation surfaces in affine 3-space R 3 where one of the three summands in the centroaffine theorema egregium is constant, and then give the classifications by solving certain partial differential equations. Mathematics Subject Classification (2000). Primary 53A15.

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“…A reference for Vol. 79, 2004 Projectively flat affine surfaces 33 affine translation surfaces is [11]. Projective flatness is preserved under homotheties, so it is sufficient to carry out classifications up to affine (and not unimodular) equivalences.…”

Section: Introductionmentioning

confidence: 99%

Projectively flat affine surfaces

Binder

2004

Journal of Geometry

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We study non-degenerate affine surfaces in A 3 with a projectively flat induced connection. The curvature of the affine metricK, the affine mean curvature H , and the Pick invariant J are related byK = H + J . Depending on the rank of the span of the gradients of these functions, a local classification of three groups is given. The main result is the characterization of the projectively flat but not locally symmetric surfaces as a solution of a system of ODEs. In the final part, we classify projectively flat and locally symmetric affine translation surfaces. (2000): Primary 53A15; Secondary 53B05. Mathematics Subject Classification

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Translationsfl�chen in der �quiaffinen Differentialgeometrie

Cited by 7 publications

References 6 publications

Linear Weingarten centroaffine translation surfaces in R3

Linear Weingarten centroaffine translation surfaces in R3

Centroaffine Translation Surfaces in $${\mathbb{R}}^3$$

Projectively flat affine surfaces

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