2017/12/24 by Bang-Yen Chen, Sharief Deshmukh, Chen, Bang-Yen +1
Mathematics · #53A07 #53C40 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A07 #msc:53C40 #msc:53C42
paper · pdf · doi:10.48550/arxiv.1712.08951
13 pages
arxiv created 2017/12/24 · arxiv updated 2017/12/27
The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component xT of the position vector field is the most natural vector field tangent to the Euclidean submanifold M. We simply call the vector field xT the canonical vector field of the Euclidean submanifold M. In earlier articles, we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, or torse-forming. In this article we study Euclidean submanifolds with conformal canonical vector field. In particular, we characterize such submanifolds. Several applications are also given. In the last section we present three global results on complete Euclidean submanifolds with conformal canonical vector field.