Quasi-isometry between two almost contact metric manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908620944310272 |
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| author | Bhattacharyya, Arindam Ganguly, Dipen Ghosh, Paritosh Sarkar, Sumanjit |
| author_facet | Bhattacharyya, Arindam Ganguly, Dipen Ghosh, Paritosh Sarkar, Sumanjit |
| contents | In this paper the notion of quasi-isometry between two Riemannian manifolds has been introduced. This idea is also imposed to study quasi-isometry between two almost contact metric manifolds. Moving further, some curvature properties of two quasi-isometrically embedded almost contact metric manifolds, $N(k)-$contact metric manifolds and Sasakian manifolds are investigated. Next, an illustrative example of a quasi-isometry between two Sasakian structures is constructed. Finally, a relation between the scalar curvature and the quasi-isometric constants for two quasi-isometric Riemannian manifolds has been established. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_15429 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quasi-isometry between two almost contact metric manifolds Bhattacharyya, Arindam Ganguly, Dipen Ghosh, Paritosh Sarkar, Sumanjit Differential Geometry 28F65, 53C20, 53C25 In this paper the notion of quasi-isometry between two Riemannian manifolds has been introduced. This idea is also imposed to study quasi-isometry between two almost contact metric manifolds. Moving further, some curvature properties of two quasi-isometrically embedded almost contact metric manifolds, $N(k)-$contact metric manifolds and Sasakian manifolds are investigated. Next, an illustrative example of a quasi-isometry between two Sasakian structures is constructed. Finally, a relation between the scalar curvature and the quasi-isometric constants for two quasi-isometric Riemannian manifolds has been established. |
| title | Quasi-isometry between two almost contact metric manifolds |
| topic | Differential Geometry 28F65, 53C20, 53C25 |
| url | https://arxiv.org/abs/2309.15429 |