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.References
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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