First Chen Inequality for CR-Warped Product Submanifolds of a Complex Space Form and Applications
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910236008251392 |
|---|---|
| author | Mustafa, Abdulqader Sati, Monika De, Uday Chand Ozel, Cenap Pigazzini, Alexander |
| author_facet | Mustafa, Abdulqader Sati, Monika De, Uday Chand Ozel, Cenap Pigazzini, Alexander |
| contents | In this paper, the first Chen inequality is proved for CR-warped product submanifolds in complex space forms. This inequality involves intrinsic invariants (a leaf-wise $δ$-invariant and the sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer to Problem [1]. We carefully distinguish the leaf-wise $δ$-invariant of a factor (used in the bound) from the intrinsic Chen invariant of the same factor, the two being related, on the totally real factor, by the Bishop--O'Neill formula. The bound is sharp and is uniform in the sign of the holomorphic sectional curvature $c$. As a geometric application, we derive necessary conditions for the immersed CR-warped product submanifold to be minimal in a complex space form, providing a partial answer to a well-known problem proposed by S.S. Chern (Problem [2]). For further research directions, we address a couple of open problems (Problem [3]} and Problem [4]). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | First Chen Inequality for CR-Warped Product Submanifolds of a Complex Space Form and Applications Mustafa, Abdulqader Sati, Monika De, Uday Chand Ozel, Cenap Pigazzini, Alexander Differential Geometry 53C15, 53C40, 53C42, 53B25 In this paper, the first Chen inequality is proved for CR-warped product submanifolds in complex space forms. This inequality involves intrinsic invariants (a leaf-wise $δ$-invariant and the sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer to Problem [1]. We carefully distinguish the leaf-wise $δ$-invariant of a factor (used in the bound) from the intrinsic Chen invariant of the same factor, the two being related, on the totally real factor, by the Bishop--O'Neill formula. The bound is sharp and is uniform in the sign of the holomorphic sectional curvature $c$. As a geometric application, we derive necessary conditions for the immersed CR-warped product submanifold to be minimal in a complex space form, providing a partial answer to a well-known problem proposed by S.S. Chern (Problem [2]). For further research directions, we address a couple of open problems (Problem [3]} and Problem [4]). |
| title | First Chen Inequality for CR-Warped Product Submanifolds of a Complex Space Form and Applications |
| topic | Differential Geometry 53C15, 53C40, 53C42, 53B25 |
| url | https://arxiv.org/abs/2605.19601 |