On mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915198142513152 |
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| author | Yan, Junhao Bi, Ran Lu, Weijun |
| author_facet | Yan, Junhao Bi, Ran Lu, Weijun |
| contents | This paper delves into the study of mixed super quasi-Einstein manifolds of dimension $n$ (for short, ${\rm M^{n}_{SQE}}$), focusing on their geometric and physical attributes. Initially, we explore several properties of ${\rm M^{n}_{SQE}}$, including conformal Ricci pseudosymmetry, Einstein's field equation, and the space-matter tensor. Subsequently, we characterize mixed super quasi-Einstein manifolds that admit Ricci-Bourguignon solitons. We establish that if the generator vector field is torse-forming, the manifold reduces to a pseudo generalized quasi-Einstein manifold, and we provide a detailed characterization of the eigenvalue problem associated with the symmetric tensor. To substantiate our findings, we construct an example to illustrate the existence of mixed super quasi-Einstein spacetime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons Yan, Junhao Bi, Ran Lu, Weijun Differential Geometry 53C15, 53C25, 53C35 This paper delves into the study of mixed super quasi-Einstein manifolds of dimension $n$ (for short, ${\rm M^{n}_{SQE}}$), focusing on their geometric and physical attributes. Initially, we explore several properties of ${\rm M^{n}_{SQE}}$, including conformal Ricci pseudosymmetry, Einstein's field equation, and the space-matter tensor. Subsequently, we characterize mixed super quasi-Einstein manifolds that admit Ricci-Bourguignon solitons. We establish that if the generator vector field is torse-forming, the manifold reduces to a pseudo generalized quasi-Einstein manifold, and we provide a detailed characterization of the eigenvalue problem associated with the symmetric tensor. To substantiate our findings, we construct an example to illustrate the existence of mixed super quasi-Einstein spacetime. |
| title | On mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons |
| topic | Differential Geometry 53C15, 53C25, 53C35 |
| url | https://arxiv.org/abs/2503.11296 |