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Manifolds with pinched 2-positive curvature perator |
Gang PENG( ), Hongliang SHAO |
| Department of Mathematics, Capital Normal University, Beijing 100048, China |
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Abstract In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of the two smallest eigenvalues of curvature operator are bounded below by δ·scal>0. If we relax the restriction of positivity of complex sectional curvature to nonnegativity, we can also show that the manifold is compact under the additional condition of positive asymptotic volume ratio.
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| Keywords
δ-pinched 2-positive curvature operator
complex sectional curvature
asymptotic volume ratio
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Corresponding Author(s):
PENG Gang,Email:penggang9521@yahoo.com.cn
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Issue Date: 01 October 2012
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