Equi-harmonic maps and Plücker formulae for horizontal-holomorphic curves on flag manifolds

2013 ◽  
Vol 193 (4) ◽  
pp. 1089-1102
Author(s):  
Lino Grama ◽  
Caio J. C. Negreiros ◽  
Luiz A. B. San Martin
Keyword(s):  
Harmonic Maps ◽  
Holomorphic Curves ◽  
Flag 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.

Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics

2011 ◽  
Vol 10 (2) ◽  
pp. 307-325 ◽  
Author(s):  
Caio J. C. Negreiros ◽  
Lino Grama ◽  
Neiton P. da Silva
Keyword(s):  
Einstein Metrics ◽  
Harmonic Maps ◽  
Flag Manifolds

Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds

2011 ◽  
Vol 40 (1) ◽  
pp. 105-123 ◽  
Author(s):  
Caio J. C. Negreiros ◽  
Lino Grama ◽  
Luiz A. B. San Martin
Keyword(s):  
Holomorphic Curves ◽  
Flag Manifolds ◽  
Hermitian Structures

Harmonic maps into periodic flag manifolds and into loop groups

1990 ◽  
Vol 7 (3) ◽  
pp. 339-361
Author(s):  
Caio J.C. Negreiros
Keyword(s):  
Harmonic Maps ◽  
Flag Manifolds ◽  
Loop Groups
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