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.

scholarly journals $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

Geometries and Topologies of Conformally Flat Riemannian Manifolds

2020 ◽  
Vol 46 (6) ◽  
pp. 1683-1695
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifolds ◽  
Conformally Flat

scholarly journals Exact solutions in Weyl-cubed gravity

2019 ◽  
Vol 34 (05) ◽  
pp. 1950036
Author(s):  
Mohammad A. Ganjali
Keyword(s):  
Exact Solutions ◽  
Order Term ◽  
Equations Of Motion ◽  
Classical Solutions ◽  
Conformally Flat ◽  
Third Order ◽  
Gravitational Action

In this paper, we will use a unitary gravitational action up to third-order of curvature with respect to the holographic a-theorem. In particular, its third-order term has a Weyl-cubed term. In this paper, we study this Weyl-cubed theory and find some of its exact classical solutions. We show that the theory admits conformally flat, Lifshitz, Schrödinger and also hyperscaling-violating backgrounds as the solutions of the equations of motion. Our analysis has been done for the pure Weyl-cubed gravity, Einstein plus Weyl-cubed term and gravity with matter.

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