Applications of differential equations to characterize the base of warped product submanifolds of cosymplectic space forms

[摘要] In the present, we first obtain Chen–Ricci inequality for C-totally real warped product submanifolds in cosymplectic space forms. Then, we focus on characterizing spheres and Euclidean spaces, by using the Bochner formula and a second-order ordinary differential equation with geometric inequalities. We derive the characterization for the base of the warped product via the first eigenvalue of the warping function. Also, it proves that there is an isometry between the base $\mathbb{N}_{1}$ and the Euclidean sphere $\mathbb{S}^{m_{1}}$ under some different extrinsic conditions.

[学科分类] 电力

[关键词] Warped product submanifolds;Cosymplectic space forms;Obata differential equation;Isometric;Geometric inequalities