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Curvature Bounds for the Spectrum of Closed Einstein Spaces

Published online by Cambridge University Press:  20 November 2018

Udo Simon
Udo Simon*
Affiliation:
Technische Universitdt Berlin, Berlin, West Germany
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The following is our main result.

(A) THEOREM. Let (M, g) be a closed connected Einstein space, n = dim M ≧ 2 (with constant scalar curvature R). Let K0 be the lower bound of the sectional curvature. Then either (M, g) is isometrically diffeomorphic to a sphere and the first nonzero eigenvalue ƛ1of the Laplacian fulfils

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 5 , 01 October 1978 , pp. 1087 - 1091
Copyright
Copyright © Canadian Mathematical Society 1978

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