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Prolongations, invariants, and fundamental identities of geometric structures
http://hdl.handle.net/10935/0002006176
http://hdl.handle.net/10935/0002006176c8dbb116-b346-40a3-a182-029c09865a40
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
https://doi.org/10.1016/j.difgeo.2023.102107
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| アイテムタイプ | default_学術雑誌論文 / Journal Article(1) | |||||||||||||
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| タイトル | ||||||||||||||
| タイトル | Prolongations, invariants, and fundamental identities of geometric structures | |||||||||||||
| 言語 | en | |||||||||||||
| 言語 | ||||||||||||||
| 言語 | eng | |||||||||||||
| 資源タイプ | ||||||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||||||
| 資源タイプ | journal article | |||||||||||||
| アクセス権 | ||||||||||||||
| アクセス権 | metadata only access | |||||||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||||||||||
| 著者 |
Hong Jaehyun
× Hong Jaehyun
× 森本 徹
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| 抄録 | ||||||||||||||
| 内容記述タイプ | Abstract | |||||||||||||
| 内容記述 | Working in the framework of nilpotent geometry, we give a unified scheme for the equivalence problem of geometric structures which extends and integrates the earlier works by Cartan, Singer-Sternberg, Tanaka, and Morimoto. By giving a new formulation of the higher order geometric structures and the universal frame bundles, we reconstruct the step prolongation of Singer-Sternberg and Tanaka. We then investigate the structure function γ of the complete step prolongation of a proper geometric structure by expanding it into components γ =κ +τ+σand establish the fundamental identities for κ, τ, σ. This then enables us to study the equivalence problem of geometric structures in full generality and to extend applications largely to the geometric structures which have not necessarily Cartan connections. Among all we give an algorithm to construct a complete system of invariants for any higher order proper geometric structure of constant symbol by making use of eneralized Spencer cohomology group associated to the symbol of the geometric structure. We then discuss thoroughly the equivalence problem for geometric structure in both cases of infinite and finite type. We also give a characterization of the Cartan connections by means of the structure function τ and make clear where the Cartan connections are placed in the perspective of the step prolongations. |
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| 言語 | en | |||||||||||||
| bibliographic_information |
en : Differential Geometry and its Applications 巻 92, p. 102107, 発行日 2024 |
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| 出版者 | ||||||||||||||
| 出版者 | Elsevier BV | |||||||||||||
| 言語 | en | |||||||||||||
| item_10001_source_id_9 | ||||||||||||||
| 収録物識別子タイプ | EISSN | |||||||||||||
| 収録物識別子 | 1872-6984 | |||||||||||||
| item_10001_relation_14 | ||||||||||||||
| 識別子タイプ | DOI | |||||||||||||
| 関連識別子 | 10.1016/j.difgeo.2023.102107 | |||||||||||||
| 権利 | ||||||||||||||
| 権利情報 | © Elsevier B.V. All rights reserved. | |||||||||||||
| 言語 | en | |||||||||||||
