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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 415, Pages 39–41 (Mi znsl5683)  
On affine diameters of a convex body

V. V. Makeev, M. Yu. Zvagel'skii

St. Petersburg State University, St. Petersburg, Russia
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Abstract: It is proved that any convex body in $\mathbb R^n$ has $n$ mutually orthogonal affine diameters $d_1,\dots,d_n$ such that it is possible to shift each of them through a linear combination of direction vectors of the diameters with smaller numbers so that their translates will intersect at their common middle point.
Key words and phrases: convex body, affine diameter, flag, vector bundle.
Received: 31.12.2012
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 212, Issue 5, Pages 542–543
DOI: https://doi.org/10.1007/s10958-016-2684-6
Bibliographic databases:
Document Type: Article
UDC: 514.172
Language: Russian
Citation: V. V. Makeev, M. Yu. Zvagel'skii, “On affine diameters of a convex body”, Geometry and topology. Part 12, Zap. Nauchn. Sem. POMI, 415, POMI, St. Petersburg, 2013, 39–41; J. Math. Sci. (N. Y.), 212:5 (2016), 542–543
Citation in format AMSBIB
\Bibitem{MakZva13}
\by V.~V.~Makeev, M.~Yu.~Zvagel'skii
\paper On affine diameters of a~convex body
\inbook Geometry and topology. Part~12
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 415
\pages 39--41
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5683}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 212
\issue 5
\pages 542--543
\crossref{https://doi.org/10.1007/s10958-016-2684-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84953455360}
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