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The affine mean curvature vector for surfaces in \(\mathbb{R}^ 4\). (English) Zbl 0833.53011
The authors study nondegenerate affine surfaces in \(\mathbb{R}^4\) following the approach introduced by K. Nomizu and L. Vrancken [Int. J. Math. 4, No. 1, 127-165 (1993; Zbl 0810.53006)]. They find the relationship between the property that a surface has extremal area under certain variations and the property that the affine mean curvature vector vanishes.
Reviewer: B.Opozda (Kraków)

53A15 Affine differential geometry
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
Full Text: DOI
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