The Hopf conjecture for positively curved manifolds with discrete abelian group actions |
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Authors: | Xiaole Su |
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Institution: | School of Mathematical Sciences (& Lab. Math. Com. Sys.), Beijing Normal University, Beijing 100875, PR China |
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Abstract: | Let M be a closed even n-manifold of positive sectional curvature. The main result asserts that the Euler characteristic of M is positive, if M admits an isometric -action with prime p?p(n) (a constant depending only on n) and k satisfies any one of the following conditions: (i) and n≠12, 18 or 20; (ii) , and n≡0 mod 4 with n≠12 or 20; (iii) , and n≡0,4 or 12 mod 20 with n≠20. This generalizes some results in T. Püttmann, C. Searle, The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank, Proc. Amer. Math. Soc. 130 (2002) 163-166; X. Rong, Positively curved manifolds with almost maximal symmetry rank, Geom. Dedicata 59 (2002) 157-182; X. Rong, X. Su, The Hopf conjecture for positively curved manifolds with abelian group actions, Comm. Cont. Math. 7 (2005) 121-136]. |
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Keywords: | 53C20 |
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