A Classification of Locally Homogeneous Affine Connections with Skew-Symmetric Ricci Tensor on 2-Dimensional Manifolds

2000 ◽  
Vol 130 (2) ◽  
pp. 109-125 ◽  
Author(s):  
Oldřich Kowalski ◽  
Barbara Opozda ◽  
Zdeněk Vlášek
Keyword(s):  
Ricci Tensor ◽  
Affine Connections ◽  
Locally Homogeneous

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

scholarly journals Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

2018 ◽  
Vol 61 (3) ◽  
pp. 543-552
Author(s):  
Imsoon Jeong ◽  
Juan de Dios Pérez ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Lie Derivatives ◽  
Lie Derivation

AbstractOn a real hypersurface M in a complex two-plane Grassmannian G2() we have the Lie derivation and a differential operator of order one associated with the generalized Tanaka–Webster connection . We give a classification of real hypersurfaces M on G2() satisfying , where ξ is the Reeb vector field on M and S the Ricci tensor of M.

scholarly journals Classification of Irreducible Holonomies of Torsion-Free Affine Connections

1999 ◽  
Vol 150 (1) ◽  
pp. 77 ◽  
Author(s):  
Sergei Merkulov ◽  
Lorenz Schwachhofer
Keyword(s):  
Affine Connections ◽  
Torsion Free

scholarly journals Real hypersurfaces of a complex projective space

1986 ◽  
Vol 33 (3) ◽  
pp. 383-387 ◽  
Author(s):  
M. Kimura
Keyword(s):  
Projective Space ◽  
Ricci Tensor ◽  
Complex Projective Space ◽  
Real Hypersurfaces ◽  
Principal Curvatures ◽  
Locally Homogeneous ◽  
Complex Projective

We study real hypersurfaces M of a complex projective space and show that a condition on the derivative of the Ricci Tensor of M implies M is locally homogeneous with two or three principal curvatures.

Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor

2010 ◽  
Vol 62 (5) ◽  
pp. 1037-1057 ◽  
Author(s):  
E. Calviño-Louzao ◽  
E. García-Río ◽  
R. Vázquez-Lorenzo
Keyword(s):  
Ricci Tensor ◽  
Curvature Operator ◽  
Locally Homogeneous ◽  
Torsion Free

AbstractCorrespondence between torsion-free connections with nilpotent skew-symmetric curvature operator and IP Riemann extensions is shown. Some consequences are derived in the study of four-dimensional IP metrics and locally homogeneous affine surfaces.

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