Rigidity Results for Submanifolds in Warped Product Manifolds

Key Points

• This research aims to explore the rigidity properties of closed submanifolds within warped product manifolds.
• Analyzed closed submanifolds immersed in warped product spaces.
• Derived integral estimates involving the warping function and second fundamental form.
• Examined relationships between the fundamental form and eigenvalues of the Laplacian.
• Established an integral estimate that connects the warping function and the second fundamental form.
• Showed implications of these estimates for the eigenvalues of the Laplacian on the submanifolds.