Flows of G2-structures on contact Calabi–Yau 7-manifolds
We study the Laplacian flow and coflow on contact Calabi–Yau 7-manifolds. We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though neither eternal nor self-simil...
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| Veröffentlicht in: | Annals of global analysis and geometry 2022-09, Vol.62 (2), p.367-389 |
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| container_title | Annals of global analysis and geometry |
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| creator | Lotay, Jason D. Sá Earp, Henrique N. Saavedra, Julieth |
| description | We study the Laplacian flow and coflow on contact Calabi–Yau 7-manifolds. We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though neither eternal nor self-similar) solution of the Laplacian coflow which has an infinite time singularity of Type IIb, unless the transverse Calabi–Yau geometry is flat. The flows in each case collapse (under normalised volume) to a lower-dimensional limit, which is either
R
, for the Laplacian flow, or standard
C
3
, for the Laplacian coflow. We also study the Hitchin flow in this setting, which we show coincides with the Laplacian coflow, up to reparametrisation of time, and defines an (incomplete) Calabi–Yau structure on the spacetime track of the flow. |
| doi_str_mv | 10.1007/s10455-022-09854-0 |
| format | Article |
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R
, for the Laplacian flow, or standard
C
3
, for the Laplacian coflow. We also study the Hitchin flow in this setting, which we show coincides with the Laplacian coflow, up to reparametrisation of time, and defines an (incomplete) Calabi–Yau structure on the spacetime track of the flow.</description><identifier>ISSN: 0232-704X</identifier><identifier>EISSN: 1572-9060</identifier><identifier>DOI: 10.1007/s10455-022-09854-0</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Analysis ; Differential Geometry ; Geometry ; Global Analysis and Analysis on Manifolds ; Manifolds (mathematics) ; Mathematical Physics ; Mathematics ; Mathematics and Statistics ; Self-similarity ; Singularities ; Solitary waves</subject><ispartof>Annals of global analysis and geometry, 2022-09, Vol.62 (2), p.367-389</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-b8d687d2e63f4514e3b2d0dbaac10d99cbc098dd777b6ad5a07258316a7258bc3</citedby><cites>FETCH-LOGICAL-c319t-b8d687d2e63f4514e3b2d0dbaac10d99cbc098dd777b6ad5a07258316a7258bc3</cites><orcidid>0000-0003-0475-4494</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10455-022-09854-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10455-022-09854-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Lotay, Jason D.</creatorcontrib><creatorcontrib>Sá Earp, Henrique N.</creatorcontrib><creatorcontrib>Saavedra, Julieth</creatorcontrib><title>Flows of G2-structures on contact Calabi–Yau 7-manifolds</title><title>Annals of global analysis and geometry</title><addtitle>Ann Glob Anal Geom</addtitle><description>We study the Laplacian flow and coflow on contact Calabi–Yau 7-manifolds. We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though neither eternal nor self-similar) solution of the Laplacian coflow which has an infinite time singularity of Type IIb, unless the transverse Calabi–Yau geometry is flat. The flows in each case collapse (under normalised volume) to a lower-dimensional limit, which is either
R
, for the Laplacian flow, or standard
C
3
, for the Laplacian coflow. 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We show that the natural initial condition leads to an ancient solution of the Laplacian flow with a finite time Type I singularity which is not a soliton, whereas it produces an immortal (though neither eternal nor self-similar) solution of the Laplacian coflow which has an infinite time singularity of Type IIb, unless the transverse Calabi–Yau geometry is flat. The flows in each case collapse (under normalised volume) to a lower-dimensional limit, which is either
R
, for the Laplacian flow, or standard
C
3
, for the Laplacian coflow. We also study the Hitchin flow in this setting, which we show coincides with the Laplacian coflow, up to reparametrisation of time, and defines an (incomplete) Calabi–Yau structure on the spacetime track of the flow.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10455-022-09854-0</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0003-0475-4494</orcidid></addata></record> |
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| subjects | Analysis Differential Geometry Geometry Global Analysis and Analysis on Manifolds Manifolds (mathematics) Mathematical Physics Mathematics Mathematics and Statistics Self-similarity Singularities Solitary waves |
| title | Flows of G2-structures on contact Calabi–Yau 7-manifolds |
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