Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure
We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were c...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/14/1704 |
| _version_ | 1797526668574720000 |
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| author | Hristo Manev Mancho Manev |
| author_facet | Hristo Manev Mancho Manev |
| author_sort | Hristo Manev |
| collection | DOAJ |
| description | We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements. |
| first_indexed | 2024-03-10T09:32:36Z |
| format | Article |
| id | doaj.art-a2fdbfa885954406a81b3bd4054cc53c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:32:36Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a2fdbfa885954406a81b3bd4054cc53c2023-11-22T04:20:54ZengMDPI AGMathematics2227-73902021-07-01914170410.3390/math9141704Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex StructureHristo Manev0Mancho Manev1Department of Medical Informatics, Biostatistics and E-Learning, Faculty of Public Health, Medical University of Plovdiv, 15A Vasil Aprilov Blvd, 4002 Plovdiv, BulgariaDepartment of Medical Informatics, Biostatistics and E-Learning, Faculty of Public Health, Medical University of Plovdiv, 15A Vasil Aprilov Blvd, 4002 Plovdiv, BulgariaWe introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements.https://www.mdpi.com/2227-7390/9/14/1704para-Ricci-like solitonη-Ricci solitonpara-Einstein-like manifoldη-Einstein manifoldalmost paracontact structurealmost paracomplex structure |
| spellingShingle | Hristo Manev Mancho Manev Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure Mathematics para-Ricci-like soliton η-Ricci soliton para-Einstein-like manifold η-Einstein manifold almost paracontact structure almost paracomplex structure |
| title | Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure |
| title_full | Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure |
| title_fullStr | Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure |
| title_full_unstemmed | Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure |
| title_short | Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure |
| title_sort | para ricci like solitons on riemannian manifolds with almost paracontact structure and almost paracomplex structure |
| topic | para-Ricci-like soliton η-Ricci soliton para-Einstein-like manifold η-Einstein manifold almost paracontact structure almost paracomplex structure |
| url | https://www.mdpi.com/2227-7390/9/14/1704 |
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