CONFORMAL AND KILLING VECTOR FIELDS ON REAL SUBMANIFOLDS OF THE CANONICAL COMPLEX SPACE FORM Cm
Deshmukh, Hanana Alohali, Haila Alodan, Sharief . 2019
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 (Cm, J, < , >). In particular, using immersion ϕ:M→Cm of a compact real submanifold M and the complex structure J of the canonical complex space form (Cm, J, < ,>), we find conditions under which the tangential component of Jϕ 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 (Cm, J, h<,>).
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