TY - JOUR
T1 - Positive pinching, volume and second Betti number
AU - Fang, Fuquan
AU - Rong, Xiaochun
N1 - Funding Information:
The rst author was supported by NSFC Grant 19741002 and the Qiu-Shi Foundation. The second author was partially supported by NSF Grant DMS 9626252 and an Alfred P. Sloan Research Fellowship.
PY - 1999
Y1 - 1999
N2 - Our main theorem asserts that for all odd n ≥ 3 and 0 < δ ≤ 1, there exists a small constant, i(n, δ) > 0, such that if a simply connected n-manifold, M, with vanishing second Betti number admits a metric of sectional curvature, δ ≤ KM ≤ 1, then the injectivity radius of M is greater than i(n, δ).
AB - Our main theorem asserts that for all odd n ≥ 3 and 0 < δ ≤ 1, there exists a small constant, i(n, δ) > 0, such that if a simply connected n-manifold, M, with vanishing second Betti number admits a metric of sectional curvature, δ ≤ KM ≤ 1, then the injectivity radius of M is greater than i(n, δ).
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U2 - 10.1007/s000390050098
DO - 10.1007/s000390050098
M3 - Article
AN - SCOPUS:0000997050
SN - 1016-443X
VL - 9
SP - 641
EP - 674
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 4
ER -