The Laplacian Flow of Locally Conformal Calibrated G2-Structures
We consider the Laplacian flow of locally conformal calibrated G 2 -structures as a natural extension to these structures of the well-known Laplacian flow of calibrated G 2 -structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated G 2 ma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-01-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/8/1/7 |
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| author | Marisa Fernández Victor Manero Jonatan Sánchez |
| author_facet | Marisa Fernández Victor Manero Jonatan Sánchez |
| author_sort | Marisa Fernández |
| collection | DOAJ |
| description | We consider the Laplacian flow of locally conformal calibrated G 2 -structures as a natural extension to these structures of the well-known Laplacian flow of calibrated G 2 -structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated G 2 manifolds and, in both cases, we obtain a flow of locally conformal calibrated G 2 -structures, which are ancient solutions, that is they are defined on a time interval of the form ( − ∞ , T ) , where T > 0 is a real number. Moreover, for each of these examples, we prove that the underlying metrics g ( t ) of the solution converge smoothly, up to pull-back by time-dependent diffeomorphisms, to a flat metric as t goes to − ∞ , and they blow-up at a finite-time singularity. |
| first_indexed | 2024-04-13T09:59:11Z |
| format | Article |
| id | doaj.art-16b2ce1c03e34d66943476bab0ebc596 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-04-13T09:59:11Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-16b2ce1c03e34d66943476bab0ebc5962022-12-22T02:51:17ZengMDPI AGAxioms2075-16802019-01-0181710.3390/axioms8010007axioms8010007The Laplacian Flow of Locally Conformal Calibrated G2-StructuresMarisa Fernández0Victor Manero1Jonatan Sánchez2Departamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, SpainDepartamento de Matemáticas—IUMA, Facultad de Ciencias Humanas y de la Educación, Universidad de Zaragoza, 22003 Huesca, SpainDepartamento de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apartado 644, 48080 Bilbao, SpainWe consider the Laplacian flow of locally conformal calibrated G 2 -structures as a natural extension to these structures of the well-known Laplacian flow of calibrated G 2 -structures. We study the Laplacian flow for two explicit examples of locally conformal calibrated G 2 manifolds and, in both cases, we obtain a flow of locally conformal calibrated G 2 -structures, which are ancient solutions, that is they are defined on a time interval of the form ( − ∞ , T ) , where T > 0 is a real number. Moreover, for each of these examples, we prove that the underlying metrics g ( t ) of the solution converge smoothly, up to pull-back by time-dependent diffeomorphisms, to a flat metric as t goes to − ∞ , and they blow-up at a finite-time singularity.http://www.mdpi.com/2075-1680/8/1/7locally conformal calibrated G2-structuresLaplacian flowsolvable Lie algebras |
| spellingShingle | Marisa Fernández Victor Manero Jonatan Sánchez The Laplacian Flow of Locally Conformal Calibrated G2-Structures Axioms locally conformal calibrated G2-structures Laplacian flow solvable Lie algebras |
| title | The Laplacian Flow of Locally Conformal Calibrated G2-Structures |
| title_full | The Laplacian Flow of Locally Conformal Calibrated G2-Structures |
| title_fullStr | The Laplacian Flow of Locally Conformal Calibrated G2-Structures |
| title_full_unstemmed | The Laplacian Flow of Locally Conformal Calibrated G2-Structures |
| title_short | The Laplacian Flow of Locally Conformal Calibrated G2-Structures |
| title_sort | laplacian flow of locally conformal calibrated g2 structures |
| topic | locally conformal calibrated G2-structures Laplacian flow solvable Lie algebras |
| url | http://www.mdpi.com/2075-1680/8/1/7 |
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