## Kodai Mathematical Journal

### The isometric embedding of the augmented Teichmüller space of a Riemann surface into the augmented Teichmüller space of its covering surface

#### Abstract

It is known that every finitely unbranched holomorphic covering $\pi:\widetilde{S}\rightarrow S$ of a compact Riemann surface $S$ with genus $g\geq2$ induces an isometric embedding $\Phi_{\pi} :Teich(S)\rightarrow Teich(\widetilde{S})$. By the mutual relations between Strebel rays in $Teich(S)$ and their embeddings in $Teich(\widetilde{S})$, we show that the augmented Teichmüller space $\widehat{Teich}(S)$ can be isometrically embedded in the augmented Teichmüller space $\widehat{Teich}(\widetilde{S})$.

#### Article information

Source
Kodai Math. J., Volume 42, Number 2 (2019), 376-392.

Dates
First available in Project Euclid: 2 July 2019

https://projecteuclid.org/euclid.kmj/1562032835

Digital Object Identifier
doi:10.2996/kmj/1562032835

Mathematical Reviews number (MathSciNet)
MR3981310

Zentralblatt MATH identifier
07108017

#### Citation

Hu, Guangming; Qi, Yi. The isometric embedding of the augmented Teichmüller space of a Riemann surface into the augmented Teichmüller space of its covering surface. Kodai Math. J. 42 (2019), no. 2, 376--392. doi:10.2996/kmj/1562032835. https://projecteuclid.org/euclid.kmj/1562032835