Geometric Properties and Spectral Estimates on Warped Products
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914429101146112 |
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| author | Meléndez, Josué Rodríguez-Romero, Eduardo Orozco, Jonatán Torres |
| author_facet | Meléndez, Josué Rodríguez-Romero, Eduardo Orozco, Jonatán Torres |
| contents | We establish an integral inequality for the Ricci curvature of a certain class of warped products $M\times_fN$, where the equality holds if and only if it is simply a Riemannian product. We also give a sufficient condition for the intersection of a warped product $M=\mathbb{R}\times_fP$ with a totally geodesic hypersurface $N$ in an arbitrary Riemannian space to be a totally geodesic slice of $M$. In addition, we establish some spectral estimates for the Laplacian of a submanifold $N$ that intersects a warped product in the same ambient manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Properties and Spectral Estimates on Warped Products Meléndez, Josué Rodríguez-Romero, Eduardo Orozco, Jonatán Torres Differential Geometry 53C40, 53C42 We establish an integral inequality for the Ricci curvature of a certain class of warped products $M\times_fN$, where the equality holds if and only if it is simply a Riemannian product. We also give a sufficient condition for the intersection of a warped product $M=\mathbb{R}\times_fP$ with a totally geodesic hypersurface $N$ in an arbitrary Riemannian space to be a totally geodesic slice of $M$. In addition, we establish some spectral estimates for the Laplacian of a submanifold $N$ that intersects a warped product in the same ambient manifold. |
| title | Geometric Properties and Spectral Estimates on Warped Products |
| topic | Differential Geometry 53C40, 53C42 |
| url | https://arxiv.org/abs/2603.27061 |