General Chen's first inequality and applications for Riemannian maps
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918308710711296 |
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| author | Singh, Ravindra Meena, Kiran Meena, Kapish Chand |
| author_facet | Singh, Ravindra Meena, Kiran Meena, Kapish Chand |
| contents | In this paper, we propose \textit{general Chen's first inequality} for Riemannian maps between Riemannian manifolds and manifest its equality and sharpness via non-trivial examples. We also utilize this general inequality by establishing Chen's first inequalities when the target spaces are generalized complex and generalized Sasakian space forms, including real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost $C(α)$ space forms. In addition, we estimate $δ$-invariants under all possible hypotheses on these space forms. Finally, we validate our new approach by comparing particular results with those of existing approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_10505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General Chen's first inequality and applications for Riemannian maps Singh, Ravindra Meena, Kiran Meena, Kapish Chand Differential Geometry 53B35, 53C15, 53D15 In this paper, we propose \textit{general Chen's first inequality} for Riemannian maps between Riemannian manifolds and manifest its equality and sharpness via non-trivial examples. We also utilize this general inequality by establishing Chen's first inequalities when the target spaces are generalized complex and generalized Sasakian space forms, including real, complex, real Kähler, Sasakian, Kenmotsu, cosymplectic, and almost $C(α)$ space forms. In addition, we estimate $δ$-invariants under all possible hypotheses on these space forms. Finally, we validate our new approach by comparing particular results with those of existing approaches. |
| title | General Chen's first inequality and applications for Riemannian maps |
| topic | Differential Geometry 53B35, 53C15, 53D15 |
| url | https://arxiv.org/abs/2510.10505 |