Differential Geometry of Position Vector Fields
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Authors
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Corresponding author. Email: bychen@math.msu.edu
Corresponding Author
Bang-Yen Chen
Article History
Received 20 January 2023Revised 20 March 2023
Accepted 19 October 2023
Available Online 29 November 2023
- DOI
- https://doi.org/10.55060/s.atmps.231115.001
- Keywords
- Thompson's law of natural growth
Rectifying curve
Finite type submanifold
Geometric flow
Soliton
Biharmonic submanifold
Constant ratio submanifold
Self-shrinker - Abstract
Differential geometry studies the geometry of curves, surfaces and higher dimensional smooth manifolds. For submanifolds in Euclidean spaces, the position vector is the most natural geometric object. Position vectors find applications throughout mathematics, engineering and natural sciences. The purpose of this survey article is to present six research topics in differential geometry in which the position vector plays a very important role. In addition to this, we explain the link between position vectors with mechanics, dynamics, and D’Arcy Thompson's law of natural growth in biology.
- Copyright
- © 2023 The Authors. Published by Athena International Publishing B.V.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (https://creativecommons.org/licenses/by-nc/4.0/).
Cite This Article
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TY - CONF AU - Bang-Yen Chen PY - 2023 DA - 2023/11/29 TI - Differential Geometry of Position Vector Fields BT - Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022) PB - Athena Publishing SP - 3 EP - 19 SN - 2949-9429 UR - https://doi.org/10.55060/s.atmps.231115.001 DO - https://doi.org/10.55060/s.atmps.231115.001 ID - Chen2023 ER -
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