Simply connectedness of Kähler and Riemannian manifolds via spectral estimates (with an appendix by Shiyu Zhang)
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915980460949504 |
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| author | Bei, Francesco |
| author_facet | Bei, Francesco |
| contents | Let $(M,h)$ be a compact Kähler manifold. Under a rather weak spectral positivity assumption we prove that $M$ is rationally connected and thus simply connected, projective with $h^{p,0}(M)=\{0\}$ for each $p>0$. Then, in the second part of this paper, we focus on Riemannian manifolds and we provide an appropriate spectral positivity assumption which guarantees that a compact and oriented even dimensional Riemannian manifold $(M,g)$ is a simply connected real homology sphere. Finally, in the appendix, a characterization of the rational dimension of compact Kähler manifolds in terms of the positivity of the minimal slope of the tangent bundle is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simply connectedness of Kähler and Riemannian manifolds via spectral estimates (with an appendix by Shiyu Zhang) Bei, Francesco Differential Geometry Complex Variables Let $(M,h)$ be a compact Kähler manifold. Under a rather weak spectral positivity assumption we prove that $M$ is rationally connected and thus simply connected, projective with $h^{p,0}(M)=\{0\}$ for each $p>0$. Then, in the second part of this paper, we focus on Riemannian manifolds and we provide an appropriate spectral positivity assumption which guarantees that a compact and oriented even dimensional Riemannian manifold $(M,g)$ is a simply connected real homology sphere. Finally, in the appendix, a characterization of the rational dimension of compact Kähler manifolds in terms of the positivity of the minimal slope of the tangent bundle is given. |
| title | Simply connectedness of Kähler and Riemannian manifolds via spectral estimates (with an appendix by Shiyu Zhang) |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2602.11002 |