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<p>In this paper, we study <i>i</i>-invariant 3-forms and <i>i</i>-anti-invariant 3-forms on closed almost Hermitian 6-manifolds. As for 2-forms, we define the <i>i</i>-invariant and <i>i</i>-anti-invariant cohomology subgroups of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^3_{dR}(M;\mathbb {C})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>H</mi> <mrow> <mi mathvariant="italic">dR</mi> </mrow> <mn>3</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>;</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. Similarly, we define the complex <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> pureness and fullness for <i>J</i> on 3-forms. By calculating an example, we have reason to believe that this definition is reasonable. At last, we study the complex <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> pure and full properties of <i>J</i> on 3-forms on closed almost Kähler 6-manifolds.</p>

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Some cohomology decompositions on closed almost Hermitian 6-manifolds

  • 期刊论文

  • 发表日期：

    2026年1月17日

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  • Qiang Tan

摘要

In this paper, we study i-invariant 3-forms and i-anti-invariant 3-forms on closed almost Hermitian 6-manifolds. As for 2-forms, we define the i-invariant and i-anti-invariant cohomology subgroups of \(H^3_{dR}(M;\mathbb {C})\) H dR 3 ( M ; C ) . Similarly, we define the complex \(C^\infty \) C ∞ pureness and fullness for J on 3-forms. By calculating an example, we have reason to believe that this definition is reasonable. At last, we study the complex \(C^\infty \) C ∞ pure and full properties of J on 3-forms on closed almost Kähler 6-manifolds.