Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds
We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.675/ |
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| author | Deng, Fusheng Ning, Jiafu Wang, Zhiwei Zhou, Xiangyu |
| author_facet | Deng, Fusheng Ning, Jiafu Wang, Zhiwei Zhou, Xiangyu |
| author_sort | Deng, Fusheng |
| collection | DOAJ |
| description | We show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a holomorphic vector bundle over a Stein manifold restricted to a submanifold which is negative in the sense of Griffiths (resp. Nakano) can be extended to the whole bundle with the same curvature negativity. |
| format | Article |
| id | doaj-art-1067d0dad5ec44f6a1a9e5e4f845271d |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-1067d0dad5ec44f6a1a9e5e4f845271d2025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121707171510.5802/crmath.67510.5802/crmath.675Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifoldsDeng, Fusheng0Ning, Jiafu1Wang, Zhiwei2Zhou, Xiangyu3School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. ChinaSchool of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P. R. ChinaSchool of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. ChinaInstitute of Mathematics, Academy of Mathematics and Systems Sciences and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences Beijing, 100190, P. R. China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P. R. ChinaWe show that a singular Hermitian metric on a holomorphic vector bundle over a Stein manifold which is negative in the sense of Griffiths (resp. Nakano) can be approximated by a sequence of smooth Hermitian metrics with the same curvature negativity. We also show that a smooth Hermitian metric on a holomorphic vector bundle over a Stein manifold restricted to a submanifold which is negative in the sense of Griffiths (resp. Nakano) can be extended to the whole bundle with the same curvature negativity.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.675/Approximationextensionsingular hermitian metricGriffiths negativeNakano negative |
| spellingShingle | Deng, Fusheng Ning, Jiafu Wang, Zhiwei Zhou, Xiangyu Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds Comptes Rendus. Mathématique Approximation extension singular hermitian metric Griffiths negative Nakano negative |
| title | Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds |
| title_full | Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds |
| title_fullStr | Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds |
| title_full_unstemmed | Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds |
| title_short | Approximation and extension of Hermitian metrics on holomorphic vector bundles over Stein manifolds |
| title_sort | approximation and extension of hermitian metrics on holomorphic vector bundles over stein manifolds |
| topic | Approximation extension singular hermitian metric Griffiths negative Nakano negative |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.675/ |
| work_keys_str_mv | AT dengfusheng approximationandextensionofhermitianmetricsonholomorphicvectorbundlesoversteinmanifolds AT ningjiafu approximationandextensionofhermitianmetricsonholomorphicvectorbundlesoversteinmanifolds AT wangzhiwei approximationandextensionofhermitianmetricsonholomorphicvectorbundlesoversteinmanifolds AT zhouxiangyu approximationandextensionofhermitianmetricsonholomorphicvectorbundlesoversteinmanifolds |