In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic structure on the tangent bundle of a Riemannian manifold.
| Published in | Pure and Applied Mathematics Journal (Volume 10, Issue 5) |
| DOI | 10.11648/j.pamj.20211005.11 |
| Page(s) | 104-106 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Geodesic Flow, Energy Functional, Hamiltonian Flow, Vector Bundle
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APA Style
Yang Liu. (2021). On Geodesic Flow and Energy Functional on Riemannian Manifolds. Pure and Applied Mathematics Journal, 10(5), 104-106. https://doi.org/10.11648/j.pamj.20211005.11
ACS Style
Yang Liu. On Geodesic Flow and Energy Functional on Riemannian Manifolds. Pure Appl. Math. J. 2021, 10(5), 104-106. doi: 10.11648/j.pamj.20211005.11
AMA Style
Yang Liu. On Geodesic Flow and Energy Functional on Riemannian Manifolds. Pure Appl Math J. 2021;10(5):104-106. doi: 10.11648/j.pamj.20211005.11
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Download@article{10.11648/j.pamj.20211005.11,
author = {Yang Liu},
title = {On Geodesic Flow and Energy Functional on Riemannian Manifolds},
journal = {Pure and Applied Mathematics Journal},
volume = {10},
number = {5},
pages = {104-106},
doi = {10.11648/j.pamj.20211005.11},
url = {https://doi.org/10.11648/j.pamj.20211005.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211005.11},
abstract = {In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic structure on the tangent bundle of a Riemannian manifold.},
year = {2021}
}
TY - JOUR T1 - On Geodesic Flow and Energy Functional on Riemannian Manifolds AU - Yang Liu Y1 - 2021/10/12 PY - 2021 N1 - https://doi.org/10.11648/j.pamj.20211005.11 DO - 10.11648/j.pamj.20211005.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 104 EP - 106 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20211005.11 AB - In this paper, we study the geodesic flow and the energy functional on a Riemannian manifold and show that the geodesics have minimal energy, in other words, are the minimizers of the energy functional, from the new perspective of involution, and that the geodesic flow is a Hamiltonian flow which has a close connection with the canonical symplectic structure on the tangent bundle of a Riemannian manifold. VL - 10 IS - 5 ER -
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