The Length of Harmonic Forms on a Compact Riemannian Manifold
Nagy, Paul-Andi ; Vernicos, Constantin
HAL, hal-01160279 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-04
Classification:  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG] 
@article{hal-01160279,
     author = {Nagy, Paul-Andi and Vernicos, Constantin},
     title = {The Length of Harmonic Forms on a Compact Riemannian Manifold},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01160279}
}

Nagy, Paul-Andi; Vernicos, Constantin. The Length of Harmonic Forms on a Compact Riemannian Manifold. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-01160279/