-
- Ornea Liviu
- University of Bucharest, Faculty of Mathematics Institute of Mathematics, Simion Stoilow of the Romanian Academy
-
- Verbitsky Misha
- Laboratory of Algebraic Geometry Faculty of Mathematics, National Research University HSE Université Libre de Bruxelles, Département de Mathématique
-
- Vuletescu Victor
- University of Bucharest, Faculty of Mathematics
この論文をさがす
抄録
<p>A locally conformally Kähler (LCK) manifold is a complex manifold, with a Kähler structure on its universal covering \tilde M, with the deck transform group acting on \tilde M by holomorphic homotheties. One could think of an LCK manifold as of a complex manifold with a Kähler form taking values in a local system L, called the conformal weight bundle. The L-valued cohomology of M is called Morse–Novikov cohomology; it was conjectured that (just as it happens for Kähler manifolds) the Morse–Novikov complex satisfies the ddc-lemma, which (if true) would have far-reaching consequences for the geometry of LCK manifolds. In particular, this version of ddc-lemma would imply existence of LCK potential on any LCK manifold with vanishing Morse–Novikov class of its L-valued Hermitian symplectic form. The ddc-conjecture was disproved for Vaisman manifolds by Goto. We prove that the ddc-lemma is true with coefficients in a sufficiently general power of L on any Vaisman manifold or LCK manifold with potential.</p>
収録刊行物
-
- Journal of the Mathematical Society of Japan
-
Journal of the Mathematical Society of Japan 70 (1), 409-422, 2018
一般社団法人 日本数学会
- Tweet
キーワード
詳細情報 詳細情報について
-
- CRID
- 1390282680091521152
-
- NII論文ID
- 130006334131
-
- NII書誌ID
- AA0070177X
-
- ISSN
- 18811167
- 18812333
- 00255645
-
- NDL書誌ID
- 028781312
-
- 本文言語コード
- en
-
- データソース種別
-
- JaLC
- NDL
- Crossref
- CiNii Articles
-
- 抄録ライセンスフラグ
- 使用不可