scholarly journals Sigma Models, Minimal Surfaces and Some Ricci Flat Pseudo-Riemannian Geometries

2012 ◽  
Author(s):  
Metin Gürses
Keyword(s):  
Sigma Models ◽  
Minimal Surfaces ◽  
Ricci Flat ◽  
Riemannian Geometries

scholarly journals ON THE INTEGRABILITY OF A CLASS OF MONGE–AMPÈRE EQUATIONS

2001 ◽  
Vol 13 (04) ◽  
pp. 529-543 ◽  
Author(s):  
J. C. BRUNELLI ◽  
M. GÜRSES ◽  
K. ZHELTUKHIN
Keyword(s):  
Sigma Models ◽  
Minimal Surfaces ◽  
Second Order ◽  
Lax Representation ◽  
Parameter Equation ◽  
Monge Ampere ◽  
Two Parameter

We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge–Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge–Ampère equations. Local as well nonlocal conserved densities are obtained.

scholarly journals CONFORMAL SIGMA MODELS WITH ANOMALOUS DIMENSIONS AND RICCI SOLITONS

2005 ◽  
Vol 20 (08) ◽  
pp. 577-584 ◽  
Author(s):  
MUNETO NITTA
Keyword(s):  
Sigma Models ◽  
Anomalous Dimension ◽  
Flow Equation ◽  
Line Bundles ◽  
Ricci Solitons ◽  
Kähler Metrics ◽  
Kahler Metrics ◽  
Ricci Flat ◽  
Anomalous Dimensions ◽  
Coset Spaces

We present new non-Ricci-flat Kähler metrics with U(N) and O(N) isometries as target manifolds of superconformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kähler metrics on the canonical line bundles over certain coset spaces in the limit of vanishing anomalous dimension.

scholarly journals Supersymmetric nonlinear sigma models on Ricci-flat Kähler manifolds with O(N) symmetry

2001 ◽  
Vol 515 (3-4) ◽  
pp. 421-425 ◽  
Author(s):  
Kiyoshi Higashijima ◽  
Tetsuji Kimura ◽  
Muneto Nitta
Keyword(s):  
Sigma Models ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Ricci Flat ◽  
Nonlinear Sigma Models

scholarly journals Supersymmetric black rings and non-linear sigma models

2010 ◽  
Vol 829 (1-2) ◽  
pp. 161-175 ◽  
Author(s):  
Yi-Xin Chen ◽  
Yong-Qiang Wang
Keyword(s):  
Sigma Models ◽  
Black Rings ◽  
Non Linear ◽  
Linear Sigma Models

scholarly journals Massive hyper-Kähler sigma models and BPS domain walls

2005 ◽  
Vol 68 (10) ◽  
pp. 1634-1642 ◽  
Author(s):  
M. Arai ◽  
M. Nitta ◽  
N. Sakai
Keyword(s):  
Sigma Models ◽  
Domain Walls
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