On Geometric Formality of Rationally Elliptic Manifolds in Dimensions 6 and 7

Svjetlana Terzić

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.

Keywords: geometric formality, rationally elliptic spaces

Classification (MSC2000): 53C25, 53C30

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