Mappings that preserve cones in Lobachevskii space |
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Authors: | A K Guts |
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Institution: | (1) Novosibirsk State University, USSR |
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Abstract: | Let n be n-dimensional Lobachevskii space, and {lx:x n} be a family of lines, parallel to a linel
0, 0![isin](/content/g66k559762002137/xxlarge8712.gif) n (in a given direction). Let {cx:X![isin](/content/g66k559762002137/xxlarge8712.gif) n} be a family of circular cones in n of opening with axes lX and vertex X. Then, iff: n![rarr](/content/g66k559762002137/xxlarge8594.gif) n(n>2) is a bijective mapping andf(Cx)=C
f(x), it follows thatf is a motion in the space n.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 687–694, May, 1973. |
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