Hyperbolic Superspaces and Super-Riemann Surfaces

Abstract

In this paper, we will generalize some results in Manin's paper "Three-dimensional hyperbolic geometry as $\infty$-adic Arakelov geometry" to the supergeometric setting. More precisely, viewing ${\mathbb{C}}^{1|1}$ as the boundary of the hyperbolic superspace ${\mathcal{H}}^{3|2}$, we reexpress the super-Green functions on the supersphere ${\hat{\mathbb{C}}}^{1|1}$ and the supertorus $T^{1|1}$ by some data derived from the supergeodesics in ${\mathcal{H}}^{3|2}$.

References in corpus (1)

• On the renormalized volume of hyperbolic 3-manifolds