Abstract
In the present paper, we extend the study of (Ali et al. in J. Inequal. Appl. 2020:241,
2020
) by using differential equations (García-Río et al. in J. Differ. Equ. 194(2):287–299,
2003
; Pigola et al. in Math. Z. 268:777–790,
2011
; Tanno in J. Math. Soc. Jpn. 30(3):509–531,
1978
; Tashiro in Trans. Am. Math. Soc. 117:251–275,
1965
), and we find some necessary conditions for the base of warped product submanifolds of cosymplectic space form
M
˜
2
m
+
1
(
ϵ
)
to be isometric to the Euclidean space
R
n
or a warped product of complete manifold
N
and Euclidean space
R
.