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2 2008

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Mappings preserving some distances

Billich M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2008

Vol. 13

10-14

We deal with mappings which preserve unit (some positive) distance, as well as with mappings contracting (expanding) some distance. In particular, we show that a mapping preserving three positive distances is an isometry.

Some characterization of osculating curves in the Euclidean spaces

Ilarslan K., Nesovic E.

Demonstratio Mathematica

2008

Vol. 41, nr 4

931-939

In this paper, we give some characterization for a osculating curve in 3-dimensional Euclidean space and we define a osculating curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement B1/1 of its first binormal vector field B1. In particular, we study the osculating curves in E4 and characterize such curves in terms of their curvature functions.