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<p>We investigate conformal Fedosov structures on (pseudo-) Riemannian manifolds of Roter type. Using the integrability condition for the conformal Fedosov equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\nabla \omega = \theta \otimes \omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">∇</mi> <mi>ω</mi> <mo>=</mo> <mi>θ</mi> <mo>⊗</mo> <mi>ω</mi> </mrow> </math></EquationSource> </InlineEquation>, we show that the Lee form is closed and can be gauged away, reducing the problem to the classical Fedosov case with a parallel symplectic form. By exploiting the Roter-type decomposition of the curvature tensor, we establish that any such manifold must have constant sectional curvature. In particular, conformal Fedosov structures do not exist on non-trivial Roter type manifolds. This result extends earlier non-existence theorems for symmetric, recurrent, and quasi-constant curvature manifolds to the full Roter type class, revealing the strong rigidity of conformally Fedosov geometry.</p>

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Non-existence of conformal Fedosov structures on Roter type manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月13日

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  • Patrik Peška,
  • Marek Jukl

摘要

We investigate conformal Fedosov structures on (pseudo-) Riemannian manifolds of Roter type. Using the integrability condition for the conformal Fedosov equation \(\nabla \omega = \theta \otimes \omega \) ∇ ω = θ ⊗ ω , we show that the Lee form is closed and can be gauged away, reducing the problem to the classical Fedosov case with a parallel symplectic form. By exploiting the Roter-type decomposition of the curvature tensor, we establish that any such manifold must have constant sectional curvature. In particular, conformal Fedosov structures do not exist on non-trivial Roter type manifolds. This result extends earlier non-existence theorems for symmetric, recurrent, and quasi-constant curvature manifolds to the full Roter type class, revealing the strong rigidity of conformally Fedosov geometry.