We prove that if the dimension of the first cohomology group of a RCD∗(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.
Recognizing the flat torus among RCD*(0 , N) spaces via the study of the first cohomology group / Gigli, Nicola; Rigoni, Chiara. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 57:4(2018), pp. 1-39. [10.1007/s00526-018-1377-z]
Recognizing the flat torus among RCD*(0 , N) spaces via the study of the first cohomology group
Gigli, Nicola
;Rigoni, Chiara
2018-01-01
Abstract
We prove that if the dimension of the first cohomology group of a RCD∗(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.File in questo prodotto:
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