On length and product of harmonic forms in Kähler geometry |
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Authors: | Paul-Andi Nagy |
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Affiliation: | 1. Institut für Mathematik, Humboldt Universit?t, Unter den Linden 6, 10099, Berlin, Germany 2. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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Abstract: | Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as Kähler and hyperbolic geometries are concerned. In the second part of the paper, we give algebraic and topological obstructions to the existence of a geometrically 2-formal Kähler metric, at the level of the second cohomology group. A strong interaction with almost Kähler geometry is to be noted. In complex dimension 3, we list all the possible values of the second Betti number of a geometrically 2-formal Kähler metric. |
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Keywords: | Harmonic forms K?hler manifold Almost K?hler structure |
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