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On geometric formality of rationally elliptic manifolds in dimensions 6 and 7

Terzić Svjetlana (University of Montenegro, Faculty of Science, Podgorica, Montenegro)

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 b2 = 3 has the real cohomology of a symmetric space. We also show that a rationally hyperbolic six-dimensional manifold with b2 ≤ 2 and b3 = 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.

Keywords: geometric formality, rationally elliptic spaces