On geometric formality of rationally elliitic manifolds in dimensions $6$ and $7$

Abstract

We discuss the question of geometric formality for rationally elliptic manifolds of dimension $6$ and $7$. We prove that a geometrically formal six-dimensional biquotient with $b_2=3$ has the real cohomology of a symmetric space. We also show that a rationally hyperbolic six-dimensional manifold with $b_2\le 2$ and $b_3=0$ can not be geometrically formal. As it follows from their real homotopy classification, the seven-dimensional geometrically formal rationally elliptic manifolds have the real cohomology of symmetric spaces as well.

Lemma 1 clarified and exposition improved, to appear in the Proceedings of XIX Geometrical Seminar as a special volume of Publications de l'Institute Mathematique (Beograd)

References in corpus (1)

• The classification of compact simply connected biquotients in dimension 6 and 7