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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The length of harmonic forms on a compact Riemannian manifold
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by Paul-Andi Nagy and Constantin Vernicos PDF
Trans. Amer. Math. Soc. 356 (2004), 2501-2513 Request permission

Abstract:

We study $(n+1)$-dimensional Riemannian manifolds with harmonic forms of constant length and first Betti number equal to $n$ showing that they are $2$-step nilmanifolds with some special metrics. We also characterize, 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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Additional Information
  • Paul-Andi Nagy
  • Affiliation: Université de Neuchâtel, Institut de Mathématiques, Rue Emile Argand 11, CH-2007 Neuchâtel, Switzerland
  • Address at time of publication: Humboldt-Universität zu Berlin, Institut für Mathematik, Sitz: Rudower Chaussee 25, D-10099 Berlin, Germany
  • MR Author ID: 662210
  • Email: Paul.Nagy@unine.ch, nagy@mathematik.hu-berlin.de
  • Constantin Vernicos
  • Affiliation: Université de Neuchâtel, Institut de Mathématiques, Rue Emile Argand 11, CH-2007 Neuchâtel, Switzerland
  • Email: Constantin.Vernicos@unine.ch
  • Received by editor(s): January 31, 2003
  • Received by editor(s) in revised form: April 30, 2003
  • Published electronically: January 23, 2004
  • Additional Notes: The first author was partially supported by european project ACR OFES number 00.0349
    The second author was partially supported by european project ACR OFES number 00.0349 and a grant of the FNRS 20-65060.01
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 2501-2513
  • MSC (2000): Primary 53C20, 58J50
  • DOI: https://doi.org/10.1090/S0002-9947-04-03546-9
  • MathSciNet review: 2048527