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Affinity of volume preserving mappings. (English. Russian original) Zbl 1051.53002
Mosc. Univ. Math. Bull. 56, No. 6, 8-13 (2001); translation from Vestn. Mosk. Univ., Ser. I 2001, No. 6, 10-14 (2001).
The authors show that in the second Lester theorem ([J. A. Lester, Arch. Math. 45, 561-564 (1985; Zbl 0563.51015); J. Geometry. 27, 29-35 (1986; Zbl 0595.51021); “Handbook of incidence geometry”. Chapter 16. Elsevier Science, Amsterdam, 921–944 (1995; Zbl 0826.51010)]) one may suppose that the image is located in the space of arbitrary finite dimension, and the analogue of the first Lester theorem is valid for an arbitrary \(n\), provided that any \(n\)-dimensional simplex with a unit volume is transferred in to the simplex of a unit volume.
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53A05 Surfaces in Euclidean and related spaces