On the Curvature and Heat Flow on Hamiltonian Systems
We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theore...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-01-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.2478/agms-2014-0003 |
| _version_ | 1818734925938950144 |
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| author | Ohta Shin-ichi |
| author_facet | Ohta Shin-ichi |
| author_sort | Ohta Shin-ichi |
| collection | DOAJ |
| description | We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow. |
| first_indexed | 2024-12-18T00:13:07Z |
| format | Article |
| id | doaj.art-03584fdc10964c6fb51035739f821ca4 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-18T00:13:07Z |
| publishDate | 2014-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-03584fdc10964c6fb51035739f821ca42022-12-21T21:27:37ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742014-01-012110.2478/agms-2014-0003agms-2014-0003On the Curvature and Heat Flow on Hamiltonian SystemsOhta Shin-ichi0Department of Mathematics, Kyoto University, Kyoto 606-8502, JapanWe develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.https://doi.org/10.2478/agms-2014-0003hamiltoniancurvaturecomparison theoremheat flow |
| spellingShingle | Ohta Shin-ichi On the Curvature and Heat Flow on Hamiltonian Systems Analysis and Geometry in Metric Spaces hamiltonian curvature comparison theorem heat flow |
| title | On the Curvature and Heat Flow on Hamiltonian Systems |
| title_full | On the Curvature and Heat Flow on Hamiltonian Systems |
| title_fullStr | On the Curvature and Heat Flow on Hamiltonian Systems |
| title_full_unstemmed | On the Curvature and Heat Flow on Hamiltonian Systems |
| title_short | On the Curvature and Heat Flow on Hamiltonian Systems |
| title_sort | on the curvature and heat flow on hamiltonian systems |
| topic | hamiltonian curvature comparison theorem heat flow |
| url | https://doi.org/10.2478/agms-2014-0003 |
| work_keys_str_mv | AT ohtashinichi onthecurvatureandheatflowonhamiltoniansystems |