Geodesic
Curvature Bounds for the Spectrum of Closed Einstein Spaces
Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 1087-1091

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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 
Simon, Udo. Curvature Bounds for the Spectrum of Closed Einstein Spaces. Canadian journal of mathematics, Tome 30 (1978) no. 5, pp. 1087-1091. doi: 10.4153/CJM-1978-091-8
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[1] 1. Do Carmo, M. P. and Wallach, N. R., Minimal immersions of spheres into spheres, Ann. Math. 2) 93 (1971), 43–62. Google Scholar

[2] 2. Hersch, J., Quatre propriétés isopérimétriques de membranes sphèriques homogènes, C. R. Acad. Sci. Paris, Ser. A 270 (1970), 1645–1648. Google Scholar

[3] 3. Kobayashi, S. and Nomizu, K., Foundations of differential geometry I, II (Interscience Publishers, New York, London, 1963, (1969). Google Scholar

[4] 4. Obata, M., Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333–340. Google Scholar

[5] 5. Simon, U., Isometries with spheres, Math. Z. 153 (1977), 23–27. Google Scholar

[6] 6. Simon, U., Submanifolds with parallel mean curvature vector and the curvature of minimal submanifolds of spheres, Archiv. Math. 29 (1977), 106–112. Google Scholar

[7] 7. Takahashi, T., Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380–385. Google Scholar

[8] 8. Tanno, S., On a lower bound of the second eigenvalue of the Laplacian on an Einstein space, to appear, Colloq. Math. Google Scholar

[9] 9. Yano, K. and Nagano, T., Einstein spaces admitting a one-parameter group of conformai transformations, Annals of Math. 69 (1959), 451–461. Google Scholar

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