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- Title
Euclidean Submanifolds via Tangential Components of Their Position Vector Fields.
- Authors
Bang-Yen Chen
- Abstract
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 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.
- Subjects
VECTOR fields; EUCLIDEAN algorithm; RICCI flow; SUBMANIFOLDS; RIEMANNIAN manifolds
- Publication
Mathematics (2227-7390), 2017, Vol 5, Issue 4, p51
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math5040051