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(2004 / vol.7 / no.1)
Comparison between the Teichmuller space and the Goldman space
HONG CHAN KIM
Pages. 1-12     



In this article we compare some results of
the Teichm"uller space $T(M)$ and the Goldman space $G(M)$
%which are the deformation spaces of hyperbolic structures and
%convex real projective structures
on a smooth surface $M.$
We present an algebraic expression of
an isometric embedding of $T(M)$ into $G(M)$
and show that
the modified Goldman's length parameters on $G(M)$
is an isometric extension of
the Fenchel-Nielsen's length parameter on $T(M).$



1. Introduction
2. Deformation space of $(G,X)$-structures
3. The Teichmuller space vs. the Goldman space
4. Embedding of the Teichmuller space into the Goldman space
5. Fenchel-Nielsen's and Goldman's length parameters
6. Acknowledgements



hyperbolic structure, convex real projective structure, Teichm"uller Space, Goldman Space, Hilbert metric, Poincar'e metric, length parameter



57M50, 32G15