Euclidean Submanifolds via Tangential Components of Their Position Vector Fields

Bang-Yen Chen
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Bang-Yen Chen: Department of Mathematics, Michigan State University, East Lansing, MI 48824-1027, USA

Mathematics, 2017, vol. 5, issue 4, 1-16

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.

Keywords: Euclidean submanifold; position vector field; concurrent vector field; concircular vector field; rectifying submanifold; T -submanifolds; constant ratio submanifolds; Ricci soliton (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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