On Euler number of symplectic hyperbolic manifold

被引：0

作者：

Huang, Teng ^{[1
,2
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei, Peoples R China

[2] Univ Sci & Technol China, CAS Key Lab Wu Wen Tsun Math, Hefei 230026, Anhui, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2024年 / 437卷

基金：

中国国家自然科学基金;

关键词：

Hopf conjecture; Singer conjecture; Almost Kahler manifold; Euler number; COMPACT KAHLER-MANIFOLDS; HODGE THEORY; VANISHING THEOREMS; COHOMOLOGY; L(2)-COHOMOLOGY; PARABOLICITY; EINSTEIN;

D O I：

10.1016/j.aim.2023.109445

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we introduce a class of closed 2n-dimensional almost Kahler manifold X which called the special symplectic hyperbolic manifold. Those manifolds include Kahler hyperbolic manifolds. We study the spaces of L-2-harmonic forms on the universal covering space of X. We then prove the Singer conjecture on special symplectic hyperbolic case. As an application, we can show that the Euler number of a special symplectic manifold satisfies the inequality (-1)(n)chi(X) > 0.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：30

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