Einstein manifolds of negative lower bounds on curvature operator of the second Kind
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917139764477952 |
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| author | Cheng, Haiqing Wang, Kui |
| author_facet | Cheng, Haiqing Wang, Kui |
| contents | We demonstrate that $n$-dimension closed Einstein manifolds, whose smallest eigenvalue of the curvature operator of the second kind of $\mathring{R}$ satisfies $λ_1 \ge -θ(n) \barλ$, are either flat or round spheres, where $\bar λ$ is the average of the eigenvalues of $\mathring{R}$, and $θ(n)$ is defined as in equation (1.2). Our result improves a celebrated result (Theorem 1.1) concerning Einstein manifolds with nonnegative curvature operator of the second kind. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_13912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Einstein manifolds of negative lower bounds on curvature operator of the second Kind Cheng, Haiqing Wang, Kui Differential Geometry We demonstrate that $n$-dimension closed Einstein manifolds, whose smallest eigenvalue of the curvature operator of the second kind of $\mathring{R}$ satisfies $λ_1 \ge -θ(n) \barλ$, are either flat or round spheres, where $\bar λ$ is the average of the eigenvalues of $\mathring{R}$, and $θ(n)$ is defined as in equation (1.2). Our result improves a celebrated result (Theorem 1.1) concerning Einstein manifolds with nonnegative curvature operator of the second kind. |
| title | Einstein manifolds of negative lower bounds on curvature operator of the second Kind |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.13912 |