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

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.
57
4
1
39
104
https://link.springer.com/article/10.1007%2Fs00526-018-1377-z
Gigli, Nicola; Rigoni, Chiara
File in questo prodotto:
File Dimensione Formato  
ToroRCD-final.pdf

embargo fino al 01/09/2019

Tipologia: Documento in Post-print
Licenza: Non specificato
Dimensione 523.44 kB
Formato Adobe PDF
523.44 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/88147
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 11
social impact