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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| Format: | Article |
| 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 |
| Summary: | 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 |
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| ISSN: | 2300-7443 |