scholarly journals Darboux Transforms of a Harmonic Inverse Mean Curvature Surface

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Katsuhiro Moriya
Keyword(s):  
Mean Curvature ◽  
Curvature Surface ◽  
Surface Of Revolution ◽  
Darboux Transforms

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution.

Classical Gauge Field Theory

2020 ◽  
pp. 71-92
Author(s):  
Daniel Canarutto
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Gauge Field Theory ◽  
Jet Bundle ◽  
Jet Bundles ◽  
Affine Bundle ◽  
Lagrangian Field Theory ◽  
Original Approach

After a sketch of Lagrangian field theory on jet bundles, the notion of a gauge field is introduced as a section of an affine bundle which is naturally constructed without any involvement with structure groups. An original approach to gauge field theory in terms of covariant differentials (alternative to the jet bundle approach) is then developed, and the adaptations needed in order to deal with general theories are laid out. A careful exposition of the replacement principle allows comparisons with approaches commonly found in the literature.

scholarly journals Darboux transforms and simple factor dressing of constant mean curvature surfaces

2012 ◽  
Vol 140 (1-2) ◽  
pp. 213-236 ◽  
Author(s):  
F. E. Burstall ◽  
J. F. Dorfmeister ◽  
K. Leschke ◽  
A. C. Quintino
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Constant Mean Curvature Surfaces ◽  
Simple Factor ◽  
Darboux Transforms
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