참고문헌
- Z. Ahsan, A symmetry property of the spacetime of general relativity in terms of the space-matter tensor, Brazilian J. Phys., 26(1996), 572-576.
- Z. Ahsan and S. A. Siddiqui, On the divergence of the space-matter tensor in general relativity, Adv. Stud. Theor. Phys., 4(2010), 543-556.
- K. Amur and Y. B. Maralabhavi, On quasi-conformally at spaces, Tensor (N.S.), 31(1977), 194-198.
- J. K. Beem and P. E. Ehrlich, Global Lorentzian geometry, Marcel Dekker, New York, 1981.
- C.-L. Bejan, Characterization of quasi-Einstein manifolds, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.), 53(2007), 67-72.
- A. L. Besse, Einstein manifolds, Ergeb. Math. Grenzgeb.,3. Folge, Bd. 10, Springer-Verlag, Berlin, Heidelberg, New York, 1987.
- M. C. Chaki, On generalized quasi-Einstein manifolds, Publ. Math. Debrecen, 58(2001), 683-691.
- M. C. Chaki, On super quasi-Einstein manifolds, Publ. Math. Debrecen, 64(2004), 481-488.
- M. C. Chaki and R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen, 57(2000), 297-306.
- B. Y. Chen and K. Yano, Special conformally at spaces and canal hypersurfaces, Tohoku Math. J., 25(1973), 177-184. https://doi.org/10.2748/tmj/1178241376
- C. J. S. Clarke, Singularities: global and local aspects. Topological properties and global structure of spacetime, Plenum Press, New York, 1986.
- U. C. De and B. K. De, On quasi-Einstein manifolds, Commun. Korean Math. Soc., 23(2008), 413-420. https://doi.org/10.4134/CKMS.2008.23.3.413
- U. C. De and G. C. Ghosh, On quasi-Einstein manifolds, Period. Math. Hungar., 48(2004), 223-231. https://doi.org/10.1023/B:MAHU.0000038977.94711.ab
- U. C. De and G. C. Ghosh, On generalized quasi-Einstein manifolds, Kyungpook Math. J., 44(2004), 607-615.
- U. C. De, N. Guha and D. Kamilya, On generalized Ricci-recurrent manifolds, Tensor (N.S.), 56(1995), 312-317.
- U. C. De, J. B. Jun and A. K. Gazi, Sasakian manifolds with quasi-conformal curvature tensor, Bull. Korean Math. Soc., 45(2008), 313-319.
-
U. C. De and S. Mallick, Spacetimes admitting
$W_2$ -curvature tensor, Int. J. Geom. Methods Mod. Phys., 11(2014), 1450030, 8 pp. - U. C. De and Y. Matsuyama, Quasi-conformally at manifolds satisfying certain conditions on the Ricci tensor, SUT J. Math., 42(2006), 295-303.
-
U. C. De and A. Sarkar, On the quasi-conformal curvature tensor of a (k,
${\mu}$ )-contact metric manifolds, Math. Rep. (Bucur.), 14(64)(2012), 115-129. - U. C. De and L. Velimirovic, Spacetimes with semisymmetric energy-momentum tensor, Internat. J. Theoret. Phys., 54(2015), 1779-1783. https://doi.org/10.1007/s10773-014-2381-5
- P. Debnath and A. Konar, On super quasi Einstein manifolds, Publ. Inst. Math., 89(103)(2011), 95-104. https://doi.org/10.2298/PIM1103095D
- B. P. Geroch, Spacetime structure from a global view point, Academic Press, New York, 1971.
- G. C. Ghosh, U. C. De and T. Q. Binh, Certain curvature restrictions on a quasi-Einstein manifold, Publ. Math. Debrecen, 69(2006), 209-217.
- S. Guha, On a perfect uid spacetime admitting quasi-conformal curvature tensor, Facta Universitatis, 3(2003), 843-849.
- S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, 1973.
- P. S. Joshi, Global aspects in gravitation and cosmology, Oxford Science Publications, Oxford University Press, New York, 1993.
- R. Maartens, Causal thermodynamics in relativity, Lectures given at the Hanno Rund Workshop on Relativity and Thermodynamics, Natal University, South Africa, June(1996), arXiv: astro-ph/9609119.
- C. A. Mantica and L. G. Molinari, Weakly Z symmetric manifolds, Acta Math. Hunger., 135(2012), 80-96. https://doi.org/10.1007/s10474-011-0166-3
- C. A. Mantica and Y. J. Suh, Conformally symmetric manifolds and quasi conformally recurrent Riemannian manifolds, Balkan J. Geom. Appl., 16(2011), 66-77.
- C. A. Mantica and Y. J. Suh, Pseudo-Z symmetric space-times, J. Math. Phys., 55(2014), 042502, 12 pp.
- A. L. Mocanu, Les varietes a courbure quasi-constant de type Vranceanu, Lucr. Conf. Nat. de. Geom. Si Top., Tirgoviste, 1987.
- M. Novello and M. J. Reboucas, The stability of a rotating universe, The Astrophysical Journal, 225(1978), 719-724. https://doi.org/10.1086/156533
- B. O'neill, Semi-Riemannian geometry. With applications to relativity, Academic Press, Inc., New York, 1983.
- C. Ozgur, On some classes of super quasi-Einstein manifolds, Chaos, Solitons Fractals, 40(2009), 1156-1161. https://doi.org/10.1016/j.chaos.2007.08.070
- C. Ozgur and S. Sular, On N(k)-quasi-Einstein manifolds satisfying certain conditions, Balkan J. Geom. Appl., 13(2008), 74-79.
- E. M. Patterson, Some theorems on Ricci-recurrent spaces, J. London Math. Soc., 27(1952), 287-295.
- A. Z. Petrov, Einstein spaces, Pergamon Press, Oxford, 1949.
- J. A. Schouten, Ricci-calculus, Springer, Berlin, 1954.
- A. A. Shaikh, On pseudo quasi-Einstein manifolds, Period Math Hungar, 59(2009), 119-146. https://doi.org/10.1007/s10998-009-0119-6
- S. Sular and C. Ozgur, Characterizations of generalized quasi-Einstein manifolds, An. St. Univ. Ovidius Constanta, 20(2012), 407-416.
- L. Tamassy and T. Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor (N.S.), 53(1993), 140-148.
- Gh. Vranceanu, Lecons des Geometrie Differential, Vol.4, Ed.de I'Academie, Bucharest, 1968.
- K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2(1968), 161-184. https://doi.org/10.4310/jdg/1214428253
- F. O. Zengin, m-Projectively at spacetimes, Math. Reports, 14(64)(2012), 363-370.