Bochner-Matsushima type identities for harmonic maps and rigidity theorems

1997 ◽  
pp. 85-98
Author(s):  
Jürgen Jost
Keyword(s):  
Harmonic Maps ◽  
Rigidity Theorems

scholarly journals Fixed point and rigidity theorems for harmonic maps into NPC spaces

2008 ◽  
Vol 141 (1) ◽  
pp. 33-57 ◽  
Author(s):  
Georgios Daskalopoulos ◽  
Chikako Mese
Keyword(s):  
Fixed Point ◽  
Harmonic Maps ◽  
Rigidity Theorems

Some rigidity theorems of harmonic maps between Finsler manifolds

2014 ◽  
Vol 25 (05) ◽  
pp. 1450043
Author(s):  
Qun He ◽  
Daxiao Zheng
Keyword(s):  
Riemannian Geometry ◽  
Harmonic Maps ◽  
Harmonic Map ◽  
Finsler Manifold ◽  
Finsler Manifolds ◽  
Rigidity Theorems

This paper is to study further properties of harmonic maps between Finsler manifolds. It is proved that any conformal harmonic map from an n(>2)-dimensional Finsler manifold to a Finsler manifold must be homothetic and some rigidity theorems for harmonic maps between Finsler manifolds are given, which improve some results in earlier papers and generalize Eells–Sampson's theorem and Sealey's theorem in Riemannian Geometry.

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.

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