Flat Almost Complex Surfaces in the Homogeneous Nearly Kähler $${\varvec{S}}^\mathbf{3}\varvec{\times } {\varvec{S}}^\mathbf{3}$$ S 3 × S 3

un 1 99 8 S 3 × S 3 acts freely on S 3 × S 3

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a conjecture of Lewis made in 1968. Results of P. A. Smith [10] and J. Milnor [5] show that a dihedral group cannot act freely on a sphere. This im...

Flat surfaces in the hyperbolic 3-space

In this paper we give a conformal representation of flat surfaces in the hyperbolic 3space using the complex structure induced by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends. Mathematics Subject Classification (1991): 53A35, 53C42

The holographic dual of AdS 3 × S 3 × S 3 × S 1

We construct the two dimensional N = (0, 4) gauge theory that lives on the world volume of D1-branes and intersecting D5-branes. We conjecture that this theory flows in the infra-red to a fixed point with large N = (4, 4) superconformal symmetry. The central charge of the conformal field theory is shown to coincide with the holographic dual of string theory compactified on AdS3 × S × S × S.

The Search for a Holographic Dual to AdS 3 × S 3 × S 3 × S 1 Sergei

Uniformization of S and Flat Singular Surfaces

We construct flat metrics in a given conformal class with prescribed singularities of real orders at marked points of a closed real surface. The singularities can be small conical, cylindrical, and large conical with possible translation component. Along these lines we give an elementary proof of the uniformization theorem for the sphere. 1. Uniformization in genus 0 and holomorphic structures ...