The Length of Harmonic Forms on a Compact Riemannian Manifold

Details The Length of Harmonic Forms on a Compact Riemannian Manifold The Length of Harmonic Forms on a Compact Riemannian Manifold

2003-01-31

arxiv.org/abs/math/0301369v1

Transactions of the American Mathematical Society, 356 (2004) no. 6, 2501-2513

Mathematics

Differential Geometry

13 pages

Scientific paper

We study $n$ dimensional Riemanniann manifolds with harmonic forms of constant length and first Betti number equal to $n-1$ showing that they are 2-steps nilmanifolds with some special metrics. We also characterise, in terms of properties on the product of harmonic forms, the left invariant metrics among them. This allows us to clarify the case of equality in the stable isosytolic inequalities in that setting. We also discuss other values of the Betti number.

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