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Pinching theorem for the first eigenvalue on positively curved manifolds. (English) Zbl 0496.53031

MSC:
53C20 Global Riemannian geometry, including pinching
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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References:
[1] Gallot, Un théorème de pincement et une estimation sur la première valeur propre du laplacien d’une variété riemannienne. C.R. Acad. Sci. (Paris) t.289, 8 série A 411-444 (1979)
[2] Grove, K., Shiohama, K.: A generalized sphere theorem. Ann. of Math.106, 201-211 (1977) · Zbl 0357.53027 · doi:10.2307/1971164
[3] Li, P., Yau, S.T.: Estimates of eigenvalues of a compact Riemannian manifold. Proc. Sym. Pure Math.36, 205-239 (1980) · Zbl 0441.58014
[4] Lichnerowicz, A.: Geometrie des groupes de transformations. Paris: Dunod 1958 · Zbl 0095.36701
[5] Pinsky, M.: A topological version of Obata’s sphere theorem. J. Differential Geometry14, 369-376 (1979) · Zbl 0461.53025
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