A new characterization of line-to-line maps in the upper plane | Zendy

Baokui Li | Zendy; Yuefei Wang | Zendy

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A new characterization of line-to-line maps in the upper plane

Author(s) -

Baokui Li,

Yuefei Wang

Publication year - 2013

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1301127l

Subject(s) - mathematics , affine transformation , affine plane (incidence geometry) , surjective function , line (geometry) , characterization (materials science) , transformation (genetics) , affine coordinate system , domain (mathematical analysis) , boundary (topology) , plane (geometry) , pure mathematics , space (punctuation) , affine space , affine geometry , geometry , mathematical analysis , optics , computer science , biochemistry , chemistry , physics , gene , operating system

The characterization of typical maps in a domain of a given space is a much harder problem than that in the whole space. In this paper, by using methods of hyperbolic and affine geometry, we give a new characterization of line-to-line maps in the upper plane. We show that a line-to-line surjection is either an affine transformation, or a composition of an affine transformation and a g-reflection. Moreover, we prove that the composition of two g-reflections with the same boundary is an affine transformation.

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