scholarly journals Conformally flat Riemannian manifolds admitting a one-parameter group of conformal transformations

1970 ◽  
Vol 4 (3) ◽  
pp. 335-337
Author(s):  
Morio Obata
Keyword(s):  
Riemannian Manifolds ◽  
Conformal Transformations ◽  
Conformally Flat ◽  
Parameter Group

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
Sign in / Sign up

Export Citation Format

Share Document