scholarly journals Holomorphic curves in algebraic manifolds

1977 ◽  
Vol 83 (4) ◽  
pp. 553-569 ◽  
Author(s):  
Bernard Shiffman
Keyword(s):  
Holomorphic Curves ◽  
Algebraic Manifolds

scholarly journals The Adjunction Inequality for Weyl-Harmonic Maps

2020 ◽  
Vol 7 (1) ◽  
pp. 129-140
Author(s):  
Robert Ream
Keyword(s):  
Minimal Surfaces ◽  
Twistor Space ◽  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Weyl Connection ◽  
Almost Kähler ◽  
Conformal Manifolds

AbstractIn 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\chi \left( {{T_f}\sum } \right) + \chi \left( {{N_f}\sum } \right) \le \pm {c_1}\left( {f*{T^{\left( {1,0} \right)}}M} \right).The ±J-holomorphic curves are automatically Weyl-minimal and satisfy the corresponding equality. These results generalize results of Eells-Salamon and Webster for minimal surfaces in Kähler 4-manifolds as well as their extension to almost-Kähler 4-manifolds by Chen-Tian, Ville, and Ma.

scholarly journals Algebraic volume density property of affine algebraic manifolds

2010 ◽  
Vol 181 (3) ◽  
pp. 605-647 ◽  
Author(s):  
Shulim Kaliman ◽  
Frank Kutzschebauch
Keyword(s):  
Volume Density ◽  
Density Property ◽  
Algebraic Manifolds
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