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<p>This paper investigates the geometric implications of locally conformal almost cosymplectic structures on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((k, \mu )'\)</EquationSource> </InlineEquation>-spaces. We prove that there exist integrable distributions <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {D}_{3}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {D}_{3}^{\perp }\)</EquationSource> </InlineEquation> such that locally conformal almost cosymplectic <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((k, \mu )'\)</EquationSource> </InlineEquation>-manifolds decompose locally as the Riemannian product of a totally geodesic manifold and a 2-dimensional totally geodesic surface with Gaussian curvature <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(-k\)</EquationSource> </InlineEquation>.</p>

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Locally conformal almost cosymplectic manifolds and nullity distributions

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Snethemba Hlobisile Maduna,
  • Fortuné Massamba

摘要

This paper investigates the geometric implications of locally conformal almost cosymplectic structures on \((k, \mu )'\) -spaces. We prove that there exist integrable distributions \(\mathcal {D}_{3}\) and \(\mathcal {D}_{3}^{\perp }\) such that locally conformal almost cosymplectic \((k, \mu )'\) -manifolds decompose locally as the Riemannian product of a totally geodesic manifold and a 2-dimensional totally geodesic surface with Gaussian curvature \(-k\) .