The Length of Harmonic Forms on a Compact Riemannian Manifold

2003/01/31 by Paul-Andi Nagy, Constantin Vernicos
Mathematics · #math.DG #math.SP #msc:53C20 #msc:58J50

paper · pdf

published as Transactions of the American Mathematical Society, 356 (2004) no. 6, 2501-2513 · 13 pages

arxiv created 2003/01/31 · arxiv updated 2009/11/30

Abstract

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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