×

zbMATH — the first resource for mathematics

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)

MSC:
53A15 Affine differential geometry
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Burstin, Math. Z. 27 pp 373– (1927)
[2] Calabi, Amer. J. Math. 104 pp 91– (1982)
[3] Klingenberg, Math Z. 54 pp 65– (1951)
[4] Klingenberg, Math Z. 54 pp 184– (1951)
[5] Harmonic surfaces in affine 4-space, preprint University of Pennsylvania
[6] Maximal Surfaces in Affine 4-space, preliminary version
[7] Nomizu, J. Mathematics 4 pp 127– (1993)
[8] Verstraelen, Michigan Math. J. 36 pp 77– (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.