Harmonic Maps in Complex Finsler Geometry

2004 ◽  
pp. 113-132 ◽  
Author(s):  
Seiki Nishikawa
Keyword(s):  
Harmonic Maps ◽  
Finsler Geometry

A Maximum Principle for Generalizations of Harmonic Maps in Hermitian, Affine, Weyl, and Finsler Geometry

2014 ◽  
Vol 25 (4) ◽  
pp. 2407-2426 ◽  
Author(s):  
Qun Chen ◽  
Jürgen Jost ◽  
Guofang Wang
Keyword(s):  
Maximum Principle ◽  
Harmonic Maps ◽  
Finsler Geometry

scholarly journals Finsler geometry modeling of complex fluids: reduction in viscous resistance

2021 ◽  
Vol 1730 (1) ◽  
pp. 012036
Author(s):  
Masahiko Okumura ◽  
Ippei Homma ◽  
Shuta Noro ◽  
Hiroshi Koibuchi
Keyword(s):  
Complex Fluids ◽  
Finsler Geometry ◽  
Viscous Resistance ◽  
Geometry Modeling

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 Finsler geometry modeling for anisotropic diffusion in Turing patterns

2021 ◽  
Vol 1730 (1) ◽  
pp. 012035
Author(s):  
Hiroshi Koibuchi ◽  
Masahiko Okumura ◽  
Shuta Noro
Keyword(s):  
Anisotropic Diffusion ◽  
Finsler Geometry ◽  
Turing Patterns ◽  
Geometry Modeling
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