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Let M be a n-dimensional \(C^\infty \) manifold, and let \(\mathscr {F}\) be a codimension q foliation of M. Let \(B_T^1 = B^1_T ({\mathscr {F}}) = B^1_T (M, \, {\mathscr {F}})\) be the total space of the transverse frame bundle \(\textrm{GL}(q, \, {\mathbb R}) \rightarrow B_T^1 \rightarrow M\) , and let \(p_T^1 : B_T^1 \rightarrow M\) be the projection. Let \(\theta ^1_T \in C^\infty \big ( T^*\big ( B^1_T \big ) \otimes {\mathbb R}^q \big )\) be the canonical 1-form, i.e.,

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Riemannian Foliations

  • 章节

  • 发表日期：

    2025年

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  • Elisabetta Barletta,
  • Sorin Dragomir,
  • Mohammad Hasan Shahid,
  • Falleh R. Al-Solamy

摘要

Let M be a n-dimensional \(C^\infty \) manifold, and let \(\mathscr {F}\) be a codimension q foliation of M. Let \(B_T^1 = B^1_T ({\mathscr {F}}) = B^1_T (M, \, {\mathscr {F}})\) be the total space of the transverse frame bundle \(\textrm{GL}(q, \, {\mathbb R}) \rightarrow B_T^1 \rightarrow M\) , and let \(p_T^1 : B_T^1 \rightarrow M\) be the projection. Let \(\theta ^1_T \in C^\infty \big ( T^*\big ( B^1_T \big ) \otimes {\mathbb R}^q \big )\) be the canonical 1-form, i.e.,