Let M-n be a compact manifold of dimension with free -action. We consider collapsings of on such that the sectional curvature and diameter of satisfy and, and give examples of collapsings for all such that the first non-zero eigenvalue of Laplacian acting on 1-forms and 2-forms of are bounded above by . Moreover, we prove that the first non-zero eigenvalue of Laplacian acting on 1-forms of all principal over is bounded below by and c(M)collapses on N.
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