본문 바로가기
KERD
논문KCI 등재

On Generalized Ricci Recurrent Spacetimes

Chiranjib Dey
경북대학교 자연과학대학 수학과|2020.09|Kyungpook Mathematical Journal|제60권 제3호|pp. 571-584|DOI 10.5666/KMJ.2020.60.3.573

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

generalized Ricci recurrent manifoldsconformally flatness
주제분류수학

초록

The object of the present paper is to characterize generalized Ricci recurrent (GR4) spacetimes. Among others things, it is proved that a conformally flat GR4 spacetime is a perfect fluid spacetime. We also prove that a GR4 spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR4 spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR4 spacetime is non-empty and a GR4 spacetime is not a trivial case.

Abstract

The object of the present paper is to characterize generalized Ricci recurrent (GR4) spacetimes. Among others things, it is proved that a conformally flat GR4 spacetime is a perfect fluid spacetime. We also prove that a GR4 spacetime with a Codazzi type Ricci tensor is a generalized Robertson Walker spacetime with Einstein fiber. We further show that in a GR4 spacetime with constant scalar curvature the energy momentum tensor is semisymmetric. Further, we obtain several corollaries. Finally, we cite some examples which are sufficient to demonstrate that the GR4 spacetime is non-empty and a GR4 spacetime is not a trivial case.

참고문헌 (41)

  1. L. Alias, "Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes", Gen. Relativity Gravitation, 27(1), pp.71~84 (1995)
  2. L. Alias, "Compact spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes", pp.67~70 (1995), World Sci. Publ.
  3. E. Boeckx, "Riemannian manifolds of conullity two" (1996), World Sci. Publ.
  4. M. Brozos-Vazquez, "Some remarks on locally conformally flat static spacetimes", J. Math. Phys, 46, pp.11~ (2005)
  5. H. A. Buchdahl, "Non-linear Lagrangians and cosmological theory", Mon. Not. Roy. Astr. Soc, 150, pp.1~8 (1970)
  6. S. Capozziello, "Cosmological perfect fluids in f(R)gravity", Int. J. Geom. Methods Mod. Phys, 16, pp.14~ (2019)
  7. M. C. Chaki, "Space-times with covariant-constant energy-momentum tensor", Internat. J. Theoret. Phys, 35, pp.1027~1032 (1996)
  8. B. -Y. Chen, "A simple characterization of generalized Robertson-Walker spacetimes", Gen. Relativity Gravitation, 46, pp.5~ (2014)
  9. A. A. Coley, "Fluid spacetimes admitting a conformal Killing vector parallel to the velocity vector", Class. Quantum Grav, 8, pp.955~968 (1991)
  10. U. C. De, "On generalized concircularly recurrent manifolds", Studia Sci. Math. Hungar, 46, pp.287~296 (2009)
  11. U. C. De, "On generalized Ricci-recurrent manifolds", Tensor(N. S. ), 56, pp.312~317 (1995)
  12. R. Deszcz, "On certain quasi-Einstein semisymmetric hypersurfaces", Ann. Univ. Sci. Budapest. E¨otv¨os Sect. Math, 41, pp.151~164 (1998)
  13. R. Deszcz, "Quasi-Einstein hypersurfaces in semiRiemannian space forms", Colloq. Math, 89(1), pp.81~97 (2001)
  14. A. De, "On conformally flat almost pseudo-Ricci symmetric spacetimes", Internat. J. Theoret. Phys, 51(9), pp.2878~2887 (2012)
  15. U. C. De, "Spacetimes with semisymmetric energy-momentum tensor", Internat. J. Theoret. Phys, 54(6), pp.1779~1783 (2015)
  16. K. L. Duggal, "Symmetries and spacetimes and Riemannian manifolds" (1999), Kluwer Academic Pub.
  17. A. Gray, "Einstein-like manifolds which are not Einstein", Geom. Dedicata, 7, pp.259~280 (1978)
  18. B. S. Guilfoyle, "Yang’s gravitational theory", Gen. Relativity Gravitation, 30(3), pp.473~495 (1998)
  19. S. W. Hawking, "The large scale structure of space-time" (1973), Cambridge University Press
  20. D. Lovelok, "Tensors, differential forms and variational principles" (1989), Dover Publ.
  21. S. Mallick, "On generalized Ricci recurrent manifolds with applications to relativity", Proc. Nat. Acad. Sci. India Sect. A, 83, pp.143~152 (2013)
  22. S. Mallick, "Spacetimes admitting W2-curvature tensor", Int. J. Geom. Methods Mod. Phys, 11(4), pp.8~ (2014)
  23. S. Mallick, "A spacetime with pseudo-projective curvature tensor", J. Math. Phys, 57(6), pp.10~ (2016)
  24. C. A. Mantica, "A second-order identity for the Riemann tensor and applications", Colloq. Math, 122(1), pp.69~82 (2011)
  25. C. A. Mantica, "Extended Derdzinski-Shen theorem for curvature tensor", Colloq. Math, 128(1), pp.1~6 (2012)
  26. C. A. Mantica, "Riemann compatible tensors", Colloq. Math, 128(2), pp.197~210 (2012)
  27. C. A. Mantica, "A condition for a perfect-fluid spacetime to be a generalized Robertson-Walker spacetime", J. Math. Phys, 57(2), pp.6~ (2016)
  28. C. A. Mantica, "Conformally symmetric manifolds and quasi conformaly recurrent Riemannian manifolds", Balkan J. Geo. Appl, 16, pp.66~77 (2011)
  29. C. A. Mantica, "Pseudo-Z symmetric space-times", J. Math. Phys, 55(4), pp.12~ (2014)
  30. Y. Matsuyama, "Compact Einstein K¨ahler submanifolds of a complex projective space", Balkan J. Geom. Appl, 14, pp.40~45 (2009)
  31. V. A. Mirzoyan, "Ricci semisymmetric submanifolds, in Russian", Itogi Nauki i Tekhniki. Ser. Probl. Geom., 23, pp.29~66 (1991)
  32. B. O’Neill, "Semi-Riemannian geometry with applications to the relativity" (1983), Academic Press
  33. E. M. Patterson, "Some theorems on Ricci-recurrent spaces", J. London Math. Soc, 27, pp.287~295 (1952)
  34. M. M. Postnikov, "Geometry VI, Riemannian geometry" (2001), Springer-Verlag
  35. M. Sanchez, "On the geometry of generalized Robertson-Walker spacetimes : geodesics", Gen. Relativity Gravitation, 30, pp.915~932 (1998)
  36. M. Sanchez, "On the geometry of generalized Robertson-Walker spacetimes : curvature and Killing fields", J. Geom. Phys, 31, pp.1~15 (1999)
  37. R. Sharma, "Proper conformal symmetries of spacetimes with divergence-free Weyl conformal tensor", J. Math. Phys, 34, pp.3582~3587 (1993)
  38. L. C. Shepley, "Spacetimes containing perfect fluids and having a vanishing conformal divergence", Comm. Math. Phys, 5, pp.237~256 (1967)
  39. H. Stephani, "Exact Solutions of Einstein’s Field equations" (2003), Cambridge Univ. Press
  40. Z. I. Szabo, "Structure theorems on Riemannian spaces satisfying R(X, Y ) · R = 0, I. The local version", J. Diff. Geom., 17, pp.531~582 (1982)
  41. A. G. Walker, "On Ruse’s spaces of recurrent curvature", Proc. London Math. Soc, 52, pp.36~64 (1950)

관련 논문AI추천

Spacetimes admitting divergence free $m$-projective curvature tensorDipankar Hazra, Uday Chand De대한수학회 · 대한수학회논문집2024 · 제39권 제1호Pseudo projective Ricci symmetric spacetimesPradip Majhi, Sahanous Mallick, Uday Chand De대한수학회 · 대한수학회논문집2018 · 제33권 제2호On Weakly Z Symmetric SpacetimesUday Chand De경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2018 · 제58권 제4호The W*-curvature Tensor on Relativistic Space-timesAbdallah Abdelhameed Syied, Hassan Abu-Donia, Sameh Shenawy경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제1호ON PSEUDO CYCLIC RICCI SYMMETRIC SPACETIMESABSOS ALI SHAIKH, SHYAMAL KUMAR HUI장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제3호Lorentzian Manifolds: A characterization with semiconformal curvature tensorChiranjib Dey, Uday Chand De대한수학회 · 대한수학회논문집2019 · 제34권 제3호

이 간행물의 다른 논문 (14건)

Variants of Essential Arity for Partial FunctionsNareupanat Lekkoksung, Erkko Lehtonenpp. 423-443φ-prime Subsemimodules of Semimodules over Commutative SemiringsFatemeh Fatahi, Reza Safakishpp. 445-453Purities of Ordered Ideals of Ordered SemiringsPakorn Palakawong na Ayutthaya, Bundit Pibaljommeepp. 455-465On Diameter, Cyclomatic Number and Inverse Degree of Chemical GraphsReza Sharafdini, Ali Reza Ashrafi, Ali Ghalavandpp. 467-475On the Fekete-Szegö Problem for Starlike Functions of Complex OrderHanan Darwish, Abdel-Moniem Lashin, Bashar Al Saeedipp. 477-484
원문 보기