Classification of Ricci tensor in space-times with a four-parameter group of motions acting on null hypersurfaces

1980 ◽  
Vol 13 (5) ◽  
pp. 1721-1728 ◽  
Author(s):  
M Abdel-Megied
Keyword(s):  
Ricci Tensor ◽  
Parameter Group ◽  
Null Hypersurfaces ◽  
Group Of Motions

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 On Einstein null hypersurfaces of $(LCS)_{n+2}$-space forms

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Ricci Tensor ◽  
Null Hypersurface ◽  
Space Forms ◽  
Null Hypersurfaces ◽  
Geometric Conditions ◽  
Null Curves ◽  
Products Of Spheres

We show that ascreen null hypersurfaces of an $(n+2)$-dimensional Lorentzian concircular structure $(LCS)_{n+2}$-manifold admits an induced Ricci tensor. We, therefore, prove, under some geometric conditions, that an Einstein ascreen null hypersurface is locally a product of null curves and products of spheres.

Geodesics in a Finsler surface with one-parameter group of motions

2016 ◽  
Vol 89 (1-2) ◽  
pp. 137-160 ◽  
Author(s):  
NOBUHIRO INNAMI ◽  
TETSUYA NAGANO ◽  
KATSUHIRO SHIOHAMA
Keyword(s):  
Parameter Group ◽  
Group Of Motions

Symmetry properties of Harrison space-times

1964 ◽  
Vol 60 (2) ◽  
pp. 259-263
Author(s):  
C. D. Collinson
Keyword(s):  
Abelian Subgroup ◽  
Space Time ◽  
Parameter Group ◽  
Symmetry Properties ◽  
Group Of Motions

AbstractAll possible symmetries of the non-degenerate Harrison space-times are found. It is shown that if such a space-time admits an r-parameter group of motions, with r > 1, then it must admit a 2-parameter Abelian subgroup.

Recurrent conformal 2-forms on pseudo-Riemannian manifolds

2014 ◽  
Vol 11 (06) ◽  
pp. 1450056 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Ricci Tensor ◽  
Higher Dimensions ◽  
Topological Properties ◽  
Lorentzian Manifolds ◽  
Differential Structure ◽  
Arbitrary Signature

In this paper, we introduce the notion of recurrent conformal 2-forms on a pseudo-Riemannian manifold of arbitrary signature. Some theorems already proved for the same differential structure on a Riemannian manifold are proven to hold in this more general contest. Moreover other interesting results are pointed out; it is proven that if the associated covector is closed, then the Ricci tensor is Riemann compatible or equivalently, Weyl compatible: these notions were recently introduced and investigated by one of the present authors. Further some new results about the vanishing of some Weyl scalars on a pseudo-Riemannian manifold are given: it turns out that they are consequence of the generalized Derdziński–Shen theorem. Topological properties involving the vanishing of Pontryagin forms and recurrent conformal 2-forms are then stated. Finally, we study the properties of recurrent conformal 2-forms on Lorentzian manifolds (space-times). Previous theorems stated on a pseudo-Riemannian manifold of arbitrary signature are then interpreted in the light of the classification of space-times in four or in higher dimensions.

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