Principal bundle structures among second order frame bundles

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• 作者：M. de Leó ; n^a ; ^{mdeleon@icmat.es" class="auth_mail" title="E-mail the corresponding author} ; A. Martí ; n Mé ; ndez^b ; ^{amartin@dma.uvigo.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：58A20 ; 58A32
• 刊名：Differential Geometry and its Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：47
• 期：Complete
• 页码：202-211
• 全文大小：332 K

文摘

Using a model for the bundle 16e6475c2e261b12e">${\hat{\mathcal{F}}}^{2}M$ of semi-holonomic second order frames of a manifold M   as an extension of the bundle e50cbc5a7a6f11fc165bd16facec" title="Click to view the MathML source">F²M${\mathcal{F}}^{2}M$ of holonomic second order frames of M  , we introduce in 16e6475c2e261b12e">${\hat{\mathcal{F}}}^{2}M$ a principal bundle structure over e50cbc5a7a6f11fc165bd16facec" title="Click to view the MathML source">F²M${\mathcal{F}}^{2}M$, the structure group being the additive group A₂(n)$A_2(n)$ of skew-symmetric bilinear maps from Rⁿ×Rⁿ${\mathbb{R}}^n\times {\mathbb{R}}^n$ into Rⁿ${\mathbb{R}}^n$. The composition of the projection of that structure with the existing projection of the bundle ${\tilde{\mathcal{F}}}^{2}M$ of non-holonomic second order frames of M   over 16e6475c2e261b12e">${\hat{\mathcal{F}}}^{2}M$ provides a principal bundle structure in ${\tilde{\mathcal{F}}}^{2}M$ over e50cbc5a7a6f11fc165bd16facec" title="Click to view the MathML source">F²M${\mathcal{F}}^{2}M$. These results close an existing gap in the theory of second order frame bundles.