Rational formal and coformal space

Question

In rational homotopy theory there are two concepts,formal and coformal spaces.I want to know example of a space which is 1)not formal and coformal, 2)rationally hyperbolic and not coformal.

Answer 1

In this paper you will find examples that fits with your first question: http://www.sciencedirect.com/science/article/pii/S0040938303000053 "Elliptic rational spaces whose cohomologies and homotopies are isomorphic" Tetsu Nishimotoa, Hiroo Shiga, Toshihiro Yamaguchi.

The authors consider a family of elliptic spaces that are not formal nor coformal. These examples are very interesting, they build two simply-connected closed smooth manifolds $M_1$, $M_2$ such that

1. they have isomorphic rational cohomology algebra,

2. they have isomorphic rational homotopy Lie algebras $\pi_*(\Omega M_i)\otimes \mathbb{Q}$,

3. they are not rationally homotopy equivalent.