Welcome to mathimatikoi.org forum; Enjoy your visit here.

Are these Riemann Surfaces biholomorphic?

Differential Geometry
Post Reply
Tsakanikas Nickos
Community Team
Community Team
Articles: 0
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

Are these Riemann Surfaces biholomorphic?

#1

Post by Tsakanikas Nickos » Sat Oct 08, 2016 12:23 pm

Examine whether the following Riemann Surfaces are biholomorphic :
  • $ \mathbb{H} \, / < z \mapsto z + 2 > $ and $ \mathbb{H} \, / < z \mapsto z + 3 > $.
  • $ \mathbb{H} \, / < z \mapsto 2z > $ and $ \mathbb{H} \, / < z \mapsto 3z > $.
where by $ < z \mapsto \frac{az+b}{cz+d} > $ we mean the subgroup of $ Aut( \mathbb{H} ) \cong PSL(2,\mathbb{R}) $ generated by the specified element.
Post Reply