Fermi-Walker transport and the Weyl connection

1999 ◽  
Vol 119 (1) ◽  
pp. 506-510
Author(s):  
B. M. Barbashov ◽  
A. B. Pestov
Keyword(s):  
Weyl Connection

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.

Weyl connection, non-Abelian gauge field, and torsion

1995 ◽  
Vol 104 (3) ◽  
pp. 1104-1107 ◽  
Author(s):  
B. M. Barbashov ◽  
A. B. Pestov
Keyword(s):  
Gauge Field ◽  
Abelian Gauge ◽  
Weyl Connection

scholarly journals Convex projective surfaces with compatible Weyl connection are hyperbolic

2020 ◽  
Vol 13 (4) ◽  
pp. 1073-1097
Author(s):  
Thomas Mettler ◽  
Gabriel P. Paternain
Keyword(s):  
Weyl Connection ◽  
Projective Surfaces

scholarly journals First-order minisuperspace model for the Faddeev formulation of gravity

2015 ◽  
Vol 30 (32) ◽  
pp. 1550174 ◽  
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Field Equations ◽  
Piecewise Constant ◽  
First Order ◽  
Weyl Connection ◽  
Type Form ◽  
Connection Type ◽  
Discrete Theory

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR. Earlier we have proposed some minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like 4-simplices or, say, cuboids into which [Formula: see text] can be decomposed. Now we study some representation of this (discrete) theory, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR.

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