The generality of closed G_2 solitons
Publication
, Journal Article
Bryant, R
Published in: Pure and Applied Mathematics Quarterly
January 31, 2024
The local generality of the space of solitons for the Laplacian flow of closed G2-structures is analyzed, and it is shown that the germs of such structures depend, up to diffeomorphism, on 16 functions of 6 variables (in the sense of É. Cartan). The method is to construct a natural exterior differential system whose integral manifolds describe such solitons and to show that it is involutive in Cartan’s sense, so that Cartan-Kähler theory can be applied. Meanwhile, it turns out that, for the more special case of gradient solitons, the natural exterior differential system is not involutive, and the generality of these structures remains a mystery.
Duke Scholars
Published In
Pure and Applied Mathematics Quarterly
ISSN
1549-6724
Publication Date
January 31, 2024
Volume
19
Issue
6
Start / End Page
2827 / 2840
Publisher
International Press
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Bryant, R. (2024). The generality of closed G_2 solitons. Pure and Applied Mathematics Quarterly, 19(6), 2827–2840.
Bryant, Robert. “The generality of closed G_2 solitons.” Edited by Shiu-Yuen Cheng, Paulo Lima-Filho, Stephen Shing-Toung Yau, and Shing-Tung Yau. Pure and Applied Mathematics Quarterly 19, no. 6 (January 31, 2024): 2827–40.
Bryant R. The generality of closed G_2 solitons. Cheng S-Y, Lima-Filho P, Yau SS-T, Yau S-T, editors. Pure and Applied Mathematics Quarterly. 2024 Jan 31;19(6):2827–40.
Bryant, Robert. “The generality of closed G_2 solitons.” Pure and Applied Mathematics Quarterly, edited by Shiu-Yuen Cheng et al., vol. 19, no. 6, International Press, Jan. 2024, pp. 2827–40.
Bryant R. The generality of closed G_2 solitons. Cheng S-Y, Lima-Filho P, Yau SS-T, Yau S-T, editors. Pure and Applied Mathematics Quarterly. International Press; 2024 Jan 31;19(6):2827–2840.
Published In
Pure and Applied Mathematics Quarterly
ISSN
1549-6724
Publication Date
January 31, 2024
Volume
19
Issue
6
Start / End Page
2827 / 2840
Publisher
International Press
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics