On some conformally einstein manifolds of dimension four
We study an important family of four-dimensional pseudo-Riemannian manifolds, i.e. generalized symmetric spaces, in terms of conformal geometry. Generalized symmetric spaces were introduced by geometers as an extension of symmetric spaces, and a detailed classification of them was presented in low d...
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| Format: | Article |
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University of Isfahan
2022-08-01
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| Series: | ریاضی و جامعه |
| Subjects: | |
| Online Access: | https://math-sci.ui.ac.ir/article_26979_87fec1d29d84e55cdd1173bcb08a493d.pdf |
| _version_ | 1797806956237291520 |
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| author | Amirhesam Zaeim Yadollah Arya Nejad Mokhtar Gheitasi |
| author_facet | Amirhesam Zaeim Yadollah Arya Nejad Mokhtar Gheitasi |
| author_sort | Amirhesam Zaeim |
| collection | DOAJ |
| description | We study an important family of four-dimensional pseudo-Riemannian manifolds, i.e. generalized symmetric spaces, in terms of conformal geometry. Generalized symmetric spaces were introduced by geometers as an extension of symmetric spaces, and a detailed classification of them was presented in low dimensions, i.e. up to four dimensions. Today, many studies have been done on this family of (pseudo)-Riemannian manifolds. Due to its relationship with the inherent geometry of space, conformal geometry has always been in focus of researchers. Therefore, many geometric features can be studied, which are established in the conformal class of space. One of these properties that is also important in physics is the property of being Einstein. As a result of this study, a general classification of conformally Einstein metrics in generalized symmetric spaces of dimension four is presented. |
| first_indexed | 2024-03-13T06:15:15Z |
| format | Article |
| id | doaj.art-1a696cf1492b4e37850b60400f61649d |
| institution | Directory Open Access Journal |
| issn | 2345-6493 2345-6507 |
| language | fas |
| last_indexed | 2024-03-13T06:15:15Z |
| publishDate | 2022-08-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | ریاضی و جامعه |
| spelling | doaj.art-1a696cf1492b4e37850b60400f61649d2023-06-11T04:27:59ZfasUniversity of Isfahanریاضی و جامعه2345-64932345-65072022-08-0172193610.22108/msci.2022.134518.151826979On some conformally einstein manifolds of dimension fourAmirhesam Zaeim0Yadollah Arya Nejad1Mokhtar Gheitasi2Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, IranDepartment of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, IranDepartment of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, IranWe study an important family of four-dimensional pseudo-Riemannian manifolds, i.e. generalized symmetric spaces, in terms of conformal geometry. Generalized symmetric spaces were introduced by geometers as an extension of symmetric spaces, and a detailed classification of them was presented in low dimensions, i.e. up to four dimensions. Today, many studies have been done on this family of (pseudo)-Riemannian manifolds. Due to its relationship with the inherent geometry of space, conformal geometry has always been in focus of researchers. Therefore, many geometric features can be studied, which are established in the conformal class of space. One of these properties that is also important in physics is the property of being Einstein. As a result of this study, a general classification of conformally Einstein metrics in generalized symmetric spaces of dimension four is presented.https://math-sci.ui.ac.ir/article_26979_87fec1d29d84e55cdd1173bcb08a493d.pdfgeneralized symmetric spaceseinstein metricconformal geometry |
| spellingShingle | Amirhesam Zaeim Yadollah Arya Nejad Mokhtar Gheitasi On some conformally einstein manifolds of dimension four ریاضی و جامعه generalized symmetric spaces einstein metric conformal geometry |
| title | On some conformally einstein manifolds of dimension four |
| title_full | On some conformally einstein manifolds of dimension four |
| title_fullStr | On some conformally einstein manifolds of dimension four |
| title_full_unstemmed | On some conformally einstein manifolds of dimension four |
| title_short | On some conformally einstein manifolds of dimension four |
| title_sort | on some conformally einstein manifolds of dimension four |
| topic | generalized symmetric spaces einstein metric conformal geometry |
| url | https://math-sci.ui.ac.ir/article_26979_87fec1d29d84e55cdd1173bcb08a493d.pdf |
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