Browse > Article
http://dx.doi.org/10.4134/CKMS.c180138

A NOTE ON CONCIRCULAR STRUCTURE SPACE-TIMES  

Mantica, Carlo Alberto (I.I.S. Lagrange)
Molinari, Luca Guido (Physics Department Universita degli Studi di Milano)
Publication Information
Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 633-635 More about this Journal
Abstract
In this note we show that Lorentzian Concircular Structure manifolds $(LCS)_n$ coincide with Generalized Robertson-Walker space-times.
Keywords
Generalized Robertson-Walker space-time; Lorentzian concircular structure; torse-forming vector; concircular vector;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 A. A. Shaikh and K. K. Baishya, On concircular structure spacetimes II, American J. Appl. Sci. 3 (2006), no. 4, 1790-1794.   DOI
2 K. Yano, Concircular geometry I-IV, Proc. Imp. Acad. Tokyo 16 (1940) 195-200, 354-360, 442-448, 505-511.   DOI
3 K. Yano, On the torse-forming directions in Riemannian spaces, Proc. Imp. Acad. Tokyo 20 (1944), 340-345.   DOI
4 L. Alas, A. Romero, and M. Sanchez, Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes, Gen. Relativity Gravitation 27 (1995), no. 1, 71-84.   DOI
5 K. Arslan, R. Deszcz, R. Ezentas, M. Hotlos, and C. Murathan, On generalized Robertson-Walker spacetimes satisfying some curvature condition, Turk. J. Math. 38 (2014) 353-373.   DOI
6 B.-Y. Chen, A simple characterization of generalized Robertson-Walker spacetimes, Gen. Relativity Gravitation 46 (2014), no. 12, Art. 1833, 5 pp.   DOI
7 A. Fialkow, Conformal geodesics, Trans. Amer. Math. Soc. 45 (1939), no. 3, 443-473.   DOI
8 M. Gutierrez and B. Olea, Global decomposition of a Lorentzian manifold as a generalized Robertson-Walker space, Differential Geom. Appl. 27 (2009), no. 1, 146-156.   DOI
9 S. K. Hui, On $\phi$-pseudo symmetries of $(LCS)_n$-manifolds, Kyungpook Math. J. 53 (2013), no. 2, 285-294.   DOI
10 C. A. Mantica and L. G. Molinari, On the Weyl and Ricci tensors of generalized Robertson-Walker space-times, J. Math. Phys. 57 (2016), no. 10, 102502, 6 pp.   DOI
11 C. A. Mantica and L. G. Molinari, Generalized Robertson-Walker spacetimes-a survey, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 3, 1730001, 27 pp.   DOI
12 A. Romero, R. M. Rubio, and J. J. Salamanca, Uniqueness of complete maximal hypersurfaces in spatially parabolic generalized Robertson-Walker spacetimes, Classical Quantum Gravity 30 (2013), no. 11, 115007, 13 pp.   DOI
13 M. Sanchez, On the geometry of generalized Robertson-Walker spacetimes: geodesics, Gen. Relativity Gravitation 30 (1998), no. 6, 915-932.   DOI
14 M. Sanchez, On the geometry of generalized Robertson-Walker spacetimes: curvature and Killing fields, J. Geom. Phys. 31 (1999), no. 1, 1-15.   DOI
15 A. A. Shaikh, On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J. 43 (2003), no. 2, 305-314.
16 A. A. Shaikh, Some results on $(LCS)_n$-manifolds, J. Korean Math. Soc. 46 (2009), no. 3, 449-461.   DOI
17 A. A. Shaikh and K. K. Baishya, On concircular structure spacetimes, J. Math. Stat. 1 (2005), no. 2, 129-132.   DOI