CYT and SKT Metrics on Compact Semi-Simple Lie Groups
A Hermitian metric on a complex manifold (, ) of complex dimension n is called Calabi-Yau with torsion (CYT) or Bismut-Ricci flat, if the restricted holonomy of the associated Bismut connection is contained in SU(), and it is called strong Kähler with torsion (SKT) or pluriclosed if the associated f...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2023 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211915 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | CYT and SKT Metrics on Compact Semi-Simple Lie Groups. Anna Fino and Gueo Grantcharov. SIGMA 19 (2023), 028, 15 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713086499094528 |
|---|---|
| author | Fino, Anna Grantcharov, Gueo |
| author_facet | Fino, Anna Grantcharov, Gueo |
| citation_txt | CYT and SKT Metrics on Compact Semi-Simple Lie Groups. Anna Fino and Gueo Grantcharov. SIGMA 19 (2023), 028, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A Hermitian metric on a complex manifold (, ) of complex dimension n is called Calabi-Yau with torsion (CYT) or Bismut-Ricci flat, if the restricted holonomy of the associated Bismut connection is contained in SU(), and it is called strong Kähler with torsion (SKT) or pluriclosed if the associated fundamental form is ∂∂¯-closed. In the paper, we study the existence of left-invariant SKT and CYT metrics on compact semi-simple Lie groups endowed with a Samelson complex structure . In particular, we show that if is determined by some maximal torus and is a left-invariant Hermitian metric, which is also invariant under the right action of the torus , and is both CYT and SKT, then g has to be Bismut flat.
|
| first_indexed | 2026-03-19T20:47:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211915 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T20:47:09Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fino, Anna Grantcharov, Gueo 2026-01-16T11:18:51Z 2023 CYT and SKT Metrics on Compact Semi-Simple Lie Groups. Anna Fino and Gueo Grantcharov. SIGMA 19 (2023), 028, 15 pages 1815-0659 2020 Mathematics Subject Classification: 53C55; 53C05; 22E25; 53C30; 53C44 arXiv:2212.07915 https://nasplib.isofts.kiev.ua/handle/123456789/211915 https://doi.org/10.3842/SIGMA.2023.028 A Hermitian metric on a complex manifold (, ) of complex dimension n is called Calabi-Yau with torsion (CYT) or Bismut-Ricci flat, if the restricted holonomy of the associated Bismut connection is contained in SU(), and it is called strong Kähler with torsion (SKT) or pluriclosed if the associated fundamental form is ∂∂¯-closed. In the paper, we study the existence of left-invariant SKT and CYT metrics on compact semi-simple Lie groups endowed with a Samelson complex structure . In particular, we show that if is determined by some maximal torus and is a left-invariant Hermitian metric, which is also invariant under the right action of the torus , and is both CYT and SKT, then g has to be Bismut flat. Anna Fino is partially supported by Project PRIN 2017 “Real and complex manifolds: Topology, Geometry and Holomorphic Dynamics”, by GNSAGA (Indam), and by a grant from the Simons Foundation (#944448). Gueo Grantcharov is partially supported by a grant from the Simons Foundation (#853269). We would like to thank the anonymous referees for the helpful comments and suggestions, as well as pointing out a confusing statement in the earlier version of the proof of Theorem3.2. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications CYT and SKT Metrics on Compact Semi-Simple Lie Groups Article published earlier |
| spellingShingle | CYT and SKT Metrics on Compact Semi-Simple Lie Groups Fino, Anna Grantcharov, Gueo |
| title | CYT and SKT Metrics on Compact Semi-Simple Lie Groups |
| title_full | CYT and SKT Metrics on Compact Semi-Simple Lie Groups |
| title_fullStr | CYT and SKT Metrics on Compact Semi-Simple Lie Groups |
| title_full_unstemmed | CYT and SKT Metrics on Compact Semi-Simple Lie Groups |
| title_short | CYT and SKT Metrics on Compact Semi-Simple Lie Groups |
| title_sort | cyt and skt metrics on compact semi-simple lie groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211915 |
| work_keys_str_mv | AT finoanna cytandsktmetricsoncompactsemisimpleliegroups AT grantcharovgueo cytandsktmetricsoncompactsemisimpleliegroups |