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### Published volumes

##### 1936-1944
Conformal and Killing vector fields on real submanifolds of the canonical complex space form $\mathbb{C}^{m}$
Volume 60, no. 2 (2019), pp. 417–430

### Abstract

In this paper, we find a conformal vector field as well as a Killing vector field on a compact real submanifold of the canonical complex space form $\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$. In particular, using immersion $\psi :M\rightarrow\mathbb{C}^{m}$ of a compact real submanifold $M$ and the complex structure $J$ of the canonical complex space form $\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$, we find conditions under which the tangential component of $J\psi$ is a conformal vector field as well as conditions under which it is a Killing vector field. Finally, we obtain a characterization of $n$-spheres in the canonical complex space form $\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$.