%0 Journal Article %J Calculus of Variations and Partial Differential Equations %D 2018 %T Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group %A Nicola Gigli %A Chiara Rigoni %X
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.
%B Calculus of Variations and Partial Differential Equations %V 57 %P 104 %8 Jun %G eng %U https://doi.org/10.1007/s00526-018-1377-z %R 10.1007/s00526-018-1377-z