{"title":"紧几乎Kähler流形上的Bott–Chern调和形式和基分解","authors":"Riccardo Piovani, Nicoletta Tardini","doi":"10.1007/s10231-023-01338-7","DOIUrl":null,"url":null,"abstract":"<div><p>Let <span>\\((X,J,\\omega )\\)</span> be a compact 2<i>n</i>-dimensional almost Kähler manifold. We prove primitive decompositions for Bott–Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott–Chern, Aeppli, Dolbeault and <span>\\(\\partial \\)</span>-harmonic forms on <span>\\((X,J,\\omega )\\)</span> are related.\n</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-023-01338-7.pdf","citationCount":"6","resultStr":"{\"title\":\"Bott–Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds\",\"authors\":\"Riccardo Piovani, Nicoletta Tardini\",\"doi\":\"10.1007/s10231-023-01338-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <span>\\\\((X,J,\\\\omega )\\\\)</span> be a compact 2<i>n</i>-dimensional almost Kähler manifold. We prove primitive decompositions for Bott–Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott–Chern, Aeppli, Dolbeault and <span>\\\\(\\\\partial \\\\)</span>-harmonic forms on <span>\\\\((X,J,\\\\omega )\\\\)</span> are related.\\n</p></div>\",\"PeriodicalId\":8265,\"journal\":{\"name\":\"Annali di Matematica Pura ed Applicata\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-05-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10231-023-01338-7.pdf\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali di Matematica Pura ed Applicata\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10231-023-01338-7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali di Matematica Pura ed Applicata","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10231-023-01338-7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Bott–Chern harmonic forms and primitive decompositions on compact almost Kähler manifolds
Let \((X,J,\omega )\) be a compact 2n-dimensional almost Kähler manifold. We prove primitive decompositions for Bott–Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott–Chern, Aeppli, Dolbeault and \(\partial \)-harmonic forms on \((X,J,\omega )\) are related.
期刊介绍：
This journal, the oldest scientific periodical in Italy, was originally edited by Barnaba Tortolini and Francesco Brioschi and has appeared since 1850. Nowadays it is managed by a nonprofit organization, the Fondazione Annali di Matematica Pura ed Applicata, c.o. Dipartimento di Matematica "U. Dini", viale Morgagni 67A, 50134 Firenze, Italy, e-mail annali@math.unifi.it).
A board of Italian university professors governs the Fondazione and appoints the editors of the journal, whose responsibility it is to supervise the refereeing process. The names of governors and editors appear on the front page of each issue. Their addresses appear in the title pages of each issue.
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