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Acta Mathematica Hungarica
Author:
P. Wang
Abstract
Let M
n
be an n(≧ 3)-dimensional compact, simply connected Riemannian manifold without boundary and S
n
be the unit sphere of the Euclidean space R
n+1. By two different means we derive an estimate of the diameter whenever the manifold considered satisfies that the sectional
curvature K
M ≦ 1, while Ric (M) ≧
\documentclass{aastex}
\usepackage{amsbsy}
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\usepackage{pifont}
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\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
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\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\tfrac{{n + 2}}{4}$$
\end{document}
and the volume V (M) ≦
\documentclass{aastex}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{mathrsfs}
\usepackage{pifont}
\usepackage{stmaryrd}
\usepackage{textcomp}
\usepackage{upgreek}
\usepackage{portland,xspace}
\usepackage{amsmath,amsxtra}
\usepackage{bbm}
\pagestyle{empty}
\DeclareMathSizes{10}{9}{7}{6}
\begin{document}
$$\tfrac{3}{2}$$
\end{document}
(1 + η)V (S
n
) for some positive number η depending only on n. Consequently, a gap phenomenon of the manifold will be given according to the estimate of the diameter.
Acta Mathematica Hungarica
Author:
P. Wang
Abstract
Based on the celebrated 1/4-pinching sphere theorem, we prove a differentiable sphere theorem on Riemannian manifolds with reverse volume pinching.
