Primitive decomposition of Bott-Chern and Dolbeault harmonic (k, k)-forms on compact almost Kahler manifolds

被引：2

作者：

Holt, Tom ^{[1
]}

Piovani, Riccardo ^{[1
]}

机构：

[1] Univ Parma, Dipartimento Sci Matemat Fis & Informat, Unita Matemat & Informat, Parco Area Sci 53-A, I-43124 Parma, Italy

来源：

EUROPEAN JOURNAL OF MATHEMATICS | 2023年 / 9卷 / 03期

关键词：

Bott-Chern Laplacian; Aeppli Laplacian; Dolbeault Laplacian; Primitive decomposition; Almost complex manifold; Harmonic forms;

D O I：

10.1007/s40879-023-00666-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the primitive decomposition of?,?, Bott-Chern and Aeppli-harmonic(k,k)-forms on compact almost K & auml;hler manifolds(M,J,?). For any D?{?,?,BC,A}, it is known that theLkP0,0component of??Hk,kDis a constant multiple of?kup to real dimension 6. In this paper we generalise this result to every dimension. We also deduce information on the componentsLk-1P1,1andLk-2P2,2of the primitive decomposition. Focusing on dimension 8, we give a full description of the spacesH2,2BCandH2,2A, from which followsH2,2BC?H2,2?andH2,2A?H2,2?.Wealso provide an almost K & auml;hler 8-dimensional example where the previous inclusions are strict and the primitive components of a harmonic form??Hk,kDare not D-harmonic, showing that the primitive decomposition of(k,k)-forms in general does not descend to harmonic forms

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页数：25

共 35 条

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