# Sur le spectre du laplacien des fibr\'es en tores qui s'effondrent

Research paper by Pierre Jammes

Indexed on: 22 Aug '05Published on: 22 Aug '05Published in: Mathematics - Differential Geometry

#### Abstract

We study the small eigenvalues of the Hodge Laplacian on collaping torus bundles with bounded curvature. In the first part of this dissertation, we consider examples of bundles on S^1 and T^2 with homogeneous structure. In the second part, we give a lower bound of the first non-zero eigenvalue of the 1-form Laplacian on principal torus bundles.