TY - JOUR T1 - Recognizing the flat torus among RCD*(0,N) spaces via the study of the first cohomology group JF - Calculus of Variations and Partial Differential Equations Y1 - 2018 A1 - Nicola Gigli A1 - Chiara Rigoni AB -

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.

VL - 57 UR - https://doi.org/10.1007/s00526-018-1377-z ER -