没有kÄhler度量的上同调kÄhler流形

IF 1 Q1 MATHEMATICS

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI:10.1155/S0161171203211327

M. Fernández, V. Muñoz, J. Santisteban

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引用次数: 22

摘要

我们给出了一些维数大于4的紧辛溶剂流形的例子，它们是上同调Kahler并且不承认Kahler度量，因为它们的基群不能是任何紧Kahler流形的基群。我们研究的一些例子被Benson和Gordon(1990)考虑过。然而，这些流形是否具有Kahler度规是一个悬而未决的问题。研究了由Auroux(1997)构造的辛子流形的形式性和硬Lefschetz性质，并讨论了一些结果。

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COHOMOLOGICALLY KÄHLER MANIFOLDS WITH NO KÄHLER METRICS

We show some examples of compact symplectic solvmanifolds, of dimension greater than four, which are cohomologically Kahler and do not admit Kahler metric since their fundamental groups cannot be the fundamental group of any compact Kahler manifold. Some of the examples that we study were considered by Benson and Gordon (1990). However, whether such manifolds have Kahler metrics was an open question. The formality and the hard Lefschetz property are studied for the symplectic submanifolds constructed by Auroux (1997) and some consequences are discussed.

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来源期刊

INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Mathematics-Mathematics (miscellaneous)

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

17 weeks

期刊介绍： The International Journal of Mathematics and Mathematical Sciences is a refereed math journal devoted to publication of original research articles, research notes, and review articles, with emphasis on contributions to unsolved problems and open questions in mathematics and mathematical sciences. All areas listed on the cover of Mathematical Reviews, such as pure and applied mathematics, mathematical physics, theoretical mechanics, probability and mathematical statistics, and theoretical biology, are included within the scope of the International Journal of Mathematics and Mathematical Sciences.