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<p>A Weitzenböck-type formula for conformally flat manifolds with nonnegative constant <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma _{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-curvature is established. Based on this, we introduce a suitable class of Riemannian manifolds, called <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {A}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">A</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-manifolds, and prove an appropriate version of the Omori-Yau maximum principle for them. As a consequence, we derive several results concerning complete <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {A}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">A</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-manifolds and establish a Catino-type integral inequality.</p>

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A Weitzenböck-Type Formula for Conformally Flat Manifolds and Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月16日

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  • Fábio R. dos Santos,
  • Elisa J. Santos

摘要

A Weitzenböck-type formula for conformally flat manifolds with nonnegative constant \(\sigma _{2}\) σ 2 -curvature is established. Based on this, we introduce a suitable class of Riemannian manifolds, called \(\mathcal {A}_{2}\) A 2 -manifolds, and prove an appropriate version of the Omori-Yau maximum principle for them. As a consequence, we derive several results concerning complete \(\mathcal {A}_{2}\) A 2 -manifolds and establish a Catino-type integral inequality.