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A manifold with positive sectional curvature and fundamental group \({\mathbb Z}_3 \oplus {\mathbb Z}_3\). (English. Russian original) Zbl 0931.53017

Sib. Math. J. 40, No. 5, 834-836 (1999); translation from Sib. Mat. Zh. 40, No. 5, 994-996 (1999).
In the article under review, the author describes a free isometric action of the group \({\mathbb Z}_3 \oplus {\mathbb Z}_3\) onto the 7-dimensional Aloff-Wallach space \(N_{1,1}\) of positive sectional curvature. The main result asserts that there exists a closed Riemannian manifold with positive sectional curvature and fundamental group \({\mathbb Z}_3 \oplus {\mathbb Z}_3\).

MSC:

53C20 Global Riemannian geometry, including pinching
57M05 Fundamental group, presentations, free differential calculus
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