Characterization of exact lumpability for vector fields on smooth manifolds

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• 作者：Leonhard Horstmeyer^a ; ^{horstmey@mis.mpg.de" class="auth_mail" title="E-mail the corresponding author} ; Fatihcan M. Atay^b ; ^{atay@member.ams.org" class="auth_mail" title="E-mail the corresponding author}
• 关键词：37C10 ; 34C40 ; 58A30 ; 53B05 ; 34A05
• 刊名：Differential Geometry and its Applications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：48
• 期：Complete
• 页码：46-60
• 全文大小：650 K

文摘

We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. We introduce a partial connection on the pullback bundle that is related to the Bott connection and behaves like a Lie derivative. The lumping conditions are formulated in terms of the differential of the lumping map, its covariant derivative with respect to the connection and their respective kernels. Some examples are discussed to illustrate the theory.