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The position vector field $\hbox{\bf x}$ 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 $\hbox{\bf x}^T$ of the position vector field is the most natural vector field tangent to the Euclidean submanifold $M$. We simply call the vector field $\hbox{\bf x}^T$ the \textit{canonical vector field} of the Euclidean submanifold $M$. In earlier articles \cite{C16,C17a,C17e,CV17,CW17}, we investigated Euclidean submanifolds whose canonical vector fields are concurrent, concircular, torse-forming, conservative or incompressible. 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.
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참고문헌 (7)
참고문헌 신청
H. Alohali / 2017 / Conformal vector fields on submanifolds of a Euclidean space / Publ. Math. Debrecen 91(1-2):217~233
B. -Y. Chen / 2016 / Differential geometry of rectifying submanifolds / Int. Electron. J. Geom 9(2):1~8
B. -Y. Chen / 2017 / Addendum to: Differential geometry of rectifying submanifolds / Int. Electron. J. Geom 10(1):81~82
B. -Y. Chen / 2017 / Topics in differential geometry associated with position vector fields on Eu-clidean submanifolds / Arab J. Math. Sci 23(1):1~17
B. -Y. Chen / 2017 / Differential geometry of concircular submanifolds of Eu-clidean spaces / Serdica Math. J 43(1):35~48
B. -Y. Chen / 2016 / Differential geometry of rectifying submanifolds / Int. Electron. J. Geom 9(2):1~8
B. -Y. Chen / 2017 / Addendum to: Differential geometry of rectifying submanifolds / Int. Electron. J. Geom 10(1):81~82
B. -Y. Chen / 2017 / Topics in differential geometry associated with position vector fields on Eu-clidean submanifolds / Arab J. Math. Sci 23(1):1~17
B. -Y. Chen / 2017 / Differential geometry of concircular submanifolds of Eu-clidean spaces / Serdica Math. J 43(1):35~48
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