Real Kaehler submanifolds in codimension up to four
| العنوان: | Real Kaehler submanifolds in codimension up to four |
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| المؤلفون: | Chion, S., Dajczer, M. |
| المصدر: | Revista Matemática Iberoamericana. |
| بيانات النشر: | European Mathematical Society - EMS - Publishing House GmbH, 2023. |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53B25, 53B35, Differential Geometry (math.DG), Mathematics::Complex Variables, General Mathematics, FOS: Mathematics, Mathematics::Differential Geometry, Mathematics::Symplectic Geometry |
| الوصف: | Let $f\colon M^{2n}\to\mathbb{R}^{2n+4}$ be an isometric immersion of a Kaehler manifold of complex dimension $n\geq 5$ into Euclidean space with complex rank at least $5$ everywhere. Our main result is that, along each connected component of an open dense subset of $M^{2n}$, either $f$ is holomorphic in $\mathbb{R}^{2n+4}\cong\mathbb{C}^{n+2}$ or it is in a unique way a composition $f=F\circ h$ of isometric immersions. In the latter case, we have that $h\colon M^{2n}\to N^{2n+2}$ is holomorphic and $F\colon N^{2n+2}\to\mathbb{R}^{2n+4}$ belongs to the class, by now quite well understood, of non-holomorphic Kaehler submanifold in codimension two. Moreover, the submanifold $F$ is minimal if and only if $f$ is minimal. Version 2 |
| تدمد: | 0213-2230 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f07bdda4928400e01cc4fe9f1fd9b3d7 https://doi.org/10.4171/rmi/1427 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....f07bdda4928400e01cc4fe9f1fd9b3d7 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 02132230 |
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