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Geometry on the Unit Ball of a Complex Hilbert Space

Published online by Cambridge University Press:  20 November 2018

Kyong T. Hahn
Kyong T. Hahn*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
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Furnishing the open unit ball of a complex Hilbert space with the Carathéodory-differential metric, we construct a model which plays a similar role as that of the Poincaré model for the hyperbolic geometry.

In this note we study the question whether or not through a point in the model not lying on a given line there exists a unique perpendicular, and give a necessary and sufficient condition for the existence of a unique perpendicular. This enables us to divide a triangle into two right triangles. Many trigonometric identities in a general triangle are easy consequences of various identities which hold on a right triangle.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 1 , 01 February 1978 , pp. 22 - 31
Copyright
Copyright © Canadian Mathematical Society 1978

References

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