Article doi/vol60/v60n2a09 - Revista de la UMA

Conformal and Killing vector fields on real submanifolds of the canonical complex space form

$\mathbb{C}^{m}$

Hanan Alohali, Haila Alodan, and Sharief Deshmukh

Volume 60, no. 2 (2019), pp. 417–430

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

$\left(\mathbb{C}^{m},J,\left\langle\,,\right\rangle\right)$ .