| Title | Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group |
| Publication Type | Journal Article |
| Year of Publication | 2018 |
| Authors | Gigli, N, Rigoni, C |
| Journal | Calculus of Variations and Partial Differential Equations |
| Volume | 57 |
| Pagination | 104 |
| Date Published | Jun |
| ISSN | 1432-0835 |
| Abstract | We prove that if the dimension of the first cohomology group of a $\mathsf{RCD}^\star (0,N)$ space is $N$, then the space is a flat torus. This generalizes a classical result due to Bochner to the non-smooth setting and also provides a first example where the study of the cohomology groups in such synthetic framework leads to geometric consequences. |
| URL | https://doi.org/10.1007/s00526-018-1377-z |
| DOI | 10.1007/s00526-018-1377-z |
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