A note on Euler number of locally conformally Kahler manifolds

被引：4
|
作者：
Huang, Teng [1 ,2 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China
[2] Chinese Acad Sci, Key Lab Wu Wen Tsun Math, Hefei 230026, Peoples R China
来源：
MATHEMATISCHE ZEITSCHRIFT | 2020年 / 296卷 / 3-4期
关键词：
LCK manifold; Euler number; PARABOLICITY;
D O I：
10.1007/s00209-020-02491-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M-2n be a compact Riemannian manifold of non-positive (resp. negative) sectional curvature. We call (M, J, theta) a d(bounded) locally conformally Kahler manifold if the lifted Lee form theta. on the universal covering space of M is d(bounded). We show that if M-2n is homeomorphic to a d(bounded) LCK manifold, then its Euler number satisfies the inequality (-1)(n) chi (M-2n) >= (resp. >) 0.
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页码：1725 / 1733
页数：9
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