Double harmonic mappings of Riemannian manifolds and its applications to stationary axisymmetric gravitational fields

1994 ◽  
Vol 33 (12) ◽  
pp. 2415-2427 ◽  
Author(s):  
Wu Ya-Bo
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Mappings ◽  
Gravitational Fields

Harmonic Mappings of Riemannian Manifolds

1964 ◽  
Vol 86 (1) ◽  
pp. 109 ◽  
Author(s):  
James Eells ◽  
J. H. Sampson
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Mappings

scholarly journals TWO-CONNECTION RENORMALIZATION AND NON-HOLONOMIC GAUGE MODELS OF EINSTEIN GRAVITY

2010 ◽  
Vol 07 (05) ◽  
pp. 713-744 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Riemannian Manifolds ◽  
Einstein Gravity ◽  
De Sitter ◽  
Renormalization Procedure ◽  
Gravitational Fields ◽  
Gauge Models ◽  
Renormalization Group Equations ◽  
Distortion Tensor ◽  
Perturbative Quantum ◽  
New Framework

A new framework for perturbative quantum gravity is proposed following the geometry of non-holonomic distributions on (pseudo)Riemannian manifolds. There are considered such distributions and adap-ted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two-loop renormalizable effective actions. We use a key result from our partner work arXiv: 0902.0911 that the classical Einstein gravity theory can be reformulated equivalently as a non-holonomic gauge model in the bundle of affine/de Sitter frames on pseudo-Riemannian space–time. It is proven that (for a class of non-holonomic constraints and splitting of the Levi–Civita connection into a "renormalizable" distinguished connection, on a base background manifold, and a gauge-like distortion tensor, in total space) a non-holonomic differential renormalization procedure for quantum gravitational fields can be elaborated. Calculation labor is reduced to one- and two-loop levels and renormalization group equations for non-holonomic configurations.

HARMONIC MAPPINGS OF RIEMANNIAN MANIFOLDS.

Harmonic Maps ◽  
1992 ◽  
pp. 1-52
Author(s):  
JAMES EELLS ◽  
J. H. SAMPSON
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Mappings

Dirichlet's boundary value problem for harmonic mappings of Riemannian manifolds

1976 ◽  
Vol 147 (3) ◽  
pp. 225-236 ◽  
Author(s):  
Stefan Hildebrandt ◽  
Helmut Kaul ◽  
Kjell-Ove Widman
Keyword(s):  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
Boundary Value ◽  
Harmonic Mappings
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