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September 10, 2025Open Access

On the Topology of Warped Product Manifolds Minimally Immersed into a Sphere

Key Points

The study reveals new results on compact warped product minimal submanifolds in spheres, expanding geometrical understanding.
Key findings include the relationship between the length and Laplacian of the warping function and its geometric properties.
This analysis builds on prior research, demonstrating the depth of geometry in minimal immersion in spheres.
Understanding these mathematical structures may have implications in differential geometry and related fields.

Abstract

In this paper, we investigate the geometry and topology of compact warped product minimal submanifolds of arbitrary codimension immersed in a sphere. These submanifolds satisfy a specific pinching condition relating the length and Laplacian of the warping function to the dimensions of the warped product. Our results extend previous work on minimal immersions into the sphere.

On the Topology of Warped Product Manifolds Minimally Immersed into a Sphere

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Abstract

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