Euclidean submanifolds via tangential components of their position vector fields
type: Item
instance of: scholarly article
title: Euclidean submanifolds via tangential components of their position vector fields
zbMATH Open document ID: 1391.37044
author: Bang-Yen Chen
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: The position vector field is the most elementary and natural geometric object on a Euclidean submanifold. The position vector field plays important roles in physics, in particular in mechanics. For instance, in any equation of motion, the position vector \(\mathbf{x}(t)\) is usually the most sought-after quantity because the position vector field defines the motion of a particle (i.e., a point mass): its location relative to a given coordinate system at some time variable \(t\). This article is a survey article. The purpose of this article is to survey recent results of Euclidean submanifolds associated with the tangential components of their position vector fields. In the last section, we present some interactions between torqued vector fields and Ricci solitons.
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 70B05
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 6898680
zbMATH Keywords: Euclidean submanifold
zbMATH Keywords: position vector field
zbMATH Keywords: concurrent vector field
zbMATH Keywords: concircular vector field
zbMATH Keywords: Ricci soliton
MaRDI profile type: Publication
full work available at URL: math5040051
OpenAlex ID: W2765256178
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DOI: 10.3390/MATH5040051
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