On differential equations classifying a warped product submanifold of cosymplectic space forms

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