The Adjunction Inequality for Weyl-Harmonic Maps
In this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal su...
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| Language: | English |
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De Gruyter
2020-03-01
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| Series: | Complex Manifolds |
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| Online Access: | https://doi.org/10.1515/coma-2020-0007 |
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doaj-a530c4d1712b485f9c3a465e988b77e22021-09-06T19:19:42ZengDe GruyterComplex Manifolds2300-74432020-03-017112914010.1515/coma-2020-0007coma-2020-0007The Adjunction Inequality for Weyl-Harmonic MapsReam Robert0Clark University Worcester, MA, United StatesIn this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequalityhttps://doi.org/10.1515/coma-2020-0007almost-complex manifoldstwistor spaceweyl geometry32q6053c2853c43 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ream Robert |
| spellingShingle |
Ream Robert The Adjunction Inequality for Weyl-Harmonic Maps Complex Manifolds almost-complex manifolds twistor space weyl geometry 32q60 53c28 53c43 |
| author_facet |
Ream Robert |
| author_sort |
Ream Robert |
| title |
The Adjunction Inequality for Weyl-Harmonic Maps |
| title_short |
The Adjunction Inequality for Weyl-Harmonic Maps |
| title_full |
The Adjunction Inequality for Weyl-Harmonic Maps |
| title_fullStr |
The Adjunction Inequality for Weyl-Harmonic Maps |
| title_full_unstemmed |
The Adjunction Inequality for Weyl-Harmonic Maps |
| title_sort |
adjunction inequality for weyl-harmonic maps |
| publisher |
De Gruyter |
| series |
Complex Manifolds |
| issn |
2300-7443 |
| publishDate |
2020-03-01 |
| description |
In this paper we study an analog of minimal surfaces called Weyl-minimal surfaces in conformal manifolds with a Weyl connection (M4, c, D). We show that there is an Eells-Salamon type correspondence between nonvertical 𝒥-holomorphic curves in the weightless twistor space and branched Weyl-minimal surfaces. When (M, c, J) is conformally almost-Hermitian, there is a canonical Weyl connection. We show that for the canonical Weyl connection, branched Weyl-minimal surfaces satisfy the adjunction inequality |
| topic |
almost-complex manifolds twistor space weyl geometry 32q60 53c28 53c43 |
| url |
https://doi.org/10.1515/coma-2020-0007 |
| work_keys_str_mv |
AT reamrobert theadjunctioninequalityforweylharmonicmaps AT reamrobert adjunctioninequalityforweylharmonicmaps |
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