Topological properties on warped product submanifolds of space forms

Key Points

• The study aims to establish sufficient conditions related to the Laplacian and gradient of the warping function for compact warped product submanifolds.
• Formulated conditions for the Laplacian and warping function's gradient.
• Analyzed the triviality of homology and fundamental groups for specific submanifolds.
• Investigated the eigenvalues of the warped function and properties of the Ricci curvature and Hessian tensor.
• Established conditions that ensure trivial homology and fundamental groups in the context of warped product submanifolds.
• Validated the instability of current flows in the fundamental group π1 of the warped product submanifold.
• Showed that the constraints apply to the eigenvalues and integral Ricci curvature of the warped function.