scholarly journals The conjectures on conformal transformations of Riemannian manifolds

1971 ◽  
Vol 6 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Morio Obata
Keyword(s):  
Riemannian Manifolds ◽  
Conformal Transformations

CONFORMALLY INVARIANT LAGRANGIANS IN METRIC-AFFINE AND RIEMANN-CARTAN SPACES

1993 ◽  
Vol 08 (29) ◽  
pp. 5141-5152 ◽  
Author(s):  
V.V. ZHYTNIKOV
Keyword(s):  
Exact Solutions ◽  
Riemannian Manifolds ◽  
Conformal Transformations ◽  
Conformally Flat ◽  
Conformally Invariant ◽  
Arbitrary Space ◽  
Nonzero Torsion

Various types of generalized conformal transformations in non-Riemannian manifolds and corresponding transformation properties of the geometrical objects are reviewed. Possible structures of conformally invariant gravity and matter Lagrangians in arbitrary space dimensions are discussed. New electrovac exact solutions of R+R2+Q2 gravity with conformally flat Bertotti-Robinson metric and nonzero torsion have been found.

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