×

zbMATH — the first resource for mathematics

Lower curvature bounds, Toponogov’s theorem, and bounded topology. II. (English) Zbl 0651.53031
This is a continuation of Part I [ibid. 18, 651-670 (1985; Zbl 0595.53043)]. In the present paper, the author improves Gromov’s “Betti number theorem” in [M. Gromov, Comment. Math. Helv. 56, 179-195 (1981; Zbl 0467.53021)] and extends it to non compact asymptotically nonnegatively curved manifolds.
Reviewer: K.Grove

MSC:
53C20 Global Riemannian geometry, including pinching
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML
References:
[1] U. ABRESCH , Lower curvature bounds, Toponogov’s theorem and bounded topology, I (Ann. Scient. Ec. Norm. Sup., Vol. 19, 1985 , pp. 651 à 670). Numdam | MR 87j:53058 | Zbl 0595.53043 · Zbl 0595.53043
[2] P. BERARD , Spectral geometry : direct and inverse problems (L.N.M., No. 1207, Springer, 1986 ). MR 88f:58146 | Zbl 0608.58001 · Zbl 0608.58001
[3] R. BISHOP and R. CRITTENDEN , Geometry of manifolds , Academic Press, N.Y., 1964 . MR 29 #6401 | Zbl 0132.16003 · Zbl 0132.16003
[4] P. BERARD and S. GALLOT , Inégalités Isopérimétriques pour l’équation de la chaleur et application à l’estimation de quelques invariants géométriques (preprint).
[5] P. BERARD and D. MEYER , Inégalités Isopérimétriques et Applications , (Ann. scient. Ec. Norm. Sup., Vol. 15, 1982 , pp. 513-542). Numdam | MR 84h:58147 | Zbl 0527.35020 · Zbl 0527.35020
[6] K. BÖRÖCZKY , Packing of spheres in spaces of constant curvature (Acta Math. Acad. Scient. Hungaricae, Vol. 32, 1978 , pp. 243-261). MR 80h:52014 | Zbl 0422.52011 · Zbl 0422.52011
[7] J. CHEEGER and D. EBIN , Comparison theorems in Riemannian geometry , North Holland, N.Y., 1975 . MR 56 #16538 | Zbl 0309.53035 · Zbl 0309.53035
[8] P. EBERLEIN and B. O’NEILL , Visibility manifolds (Pac. J. Math., Vol. 46, 1972 , pp. 45-109). Article | MR 49 #1421 | Zbl 0264.53026 · Zbl 0264.53026
[9] M. GROMOV , Curvature, diametre and Betti numbers (Comm. Math. Helv., Vol. 56, 1981 , pp. 179-195). MR 82k:53062 | Zbl 0467.53021 · Zbl 0467.53021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.