An optimal inequality between scalar curvature and spectrum of the Laplacian

Details An optimal inequality between scalar curvature and spectrum of the Laplacian An optimal inequality between scalar curvature and spectrum of the Laplacian

2002-03-26

arxiv.org/abs/math/0203271v2

Mathematics

Differential Geometry

29 pages

Scientific paper

For a Riemannian closed spin manifold and under some topological assumption (non-zero $\hat{A}$-genus or enlargeability in the sense of Gromov-Lawson), we give an optimal upper bound for the infimum of the scalar curvature in terms of the first eigenvalue of the Laplacian. The main difficulty lies in the study of the odd-dimensional case. On the other hand, we study the equality case for the closed spin Riemannian manifolds with non-zero $\hat{A}$-genus. This work improves an inequality which was first proved by K. Ono in 1988.

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