THE HYPERBOLIC SQUARE AND MÖBIUS TRANSFORMATIONS

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UNGAR A.A.

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Journal Paper

Paper Information

Journal: BANACH JOURNAL OF MATHEMATICAL ANALYSIS Year:2007 | Volume:1 | Issue:1 Page(s): 101-116

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Title

THE HYPERBOLIC SQUARE AND MÖBIUS TRANSFORMATIONS

Author(s)

UNGAR A.A.

Keywords

HYPERBOLIC SQUARE

MÖBIUS TRANSFORMATION

HYPERBOLIC GEOMETRY

GYRO GROUPS

GYRO VECTOR SPACES

Abstract

Professor Themistocles M. Rassias’ special predilection and contribution to the study of mӧbius transformations is well known. MÖBIUS TRANSFORMATIONs of the open unit disc of the complex plane and, more generally, of the open unit ball of any real inner product space, give rise to möbius addition in the ball. The latter, in turn, gives rise to möbius GYRO VECTOR SPACES that enable the Poincaré ball model of HYPERBOLIC GEOMETRY to be approached by GYRO VECTOR SPACES, in full analogy with the common vector space approach to the standard model of Euclidean geometry. The purpose of this paper, dedicated to Professor Themistocles M. Rassias, is to employ the möbius GYRO VECTOR SPACES for the introduction of the HYPERBOLIC SQUARE in the Poincare ball model of HYPERBOLIC GEOMETRY. We will find that the HYPERBOLIC SQUARE is richer in structure than its Euclidean counterpart.

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APA: Copy

UNGAR, A.A.. (2007). THE HYPERBOLIC SQUARE AND MÖBIUS TRANSFORMATIONS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 1(1), 101-116. SID. https://sid.ir/paper/316854/en

Vancouver: Copy

UNGAR A.A.. THE HYPERBOLIC SQUARE AND MÖBIUS TRANSFORMATIONS. BANACH JOURNAL OF MATHEMATICAL ANALYSIS[Internet]. 2007;1(1):101-116. Available from: https://sid.ir/paper/316854/en

IEEE: Copy

A.A. UNGAR, “THE HYPERBOLIC SQUARE AND MÖBIUS TRANSFORMATIONS,” BANACH JOURNAL OF MATHEMATICAL ANALYSIS, vol. 1, no. 1, pp. 101–116, 2007, [Online]. Available: https://sid.ir/paper/316854/en

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