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Some properties of four-dimensional Walker manifolds

Year 2017, Volume: 5 Issue: 3, 253 - 261, 01.07.2017

Abstract

In this paper, we investigate geometric properties of some curvature tensors of a four-dimensional Walker manifold. Some characterization theorems are also obtained.

References

  • Banyaga A,Massamba F (2016) Non-existence of certain Einstein metrics on some symplectic manifolds, Forum Math 28(3):527- 537.
  • Brozos-Vazquez M, Garcia-Rio E, Gilkey P, Nikevic S, Vazquez-Lorenzo R (2009) The Geometry of Walker Manifolds. Synthesis Lectures on Mathematics and Statistics, 5. (Morgan and Claypool Publishers, Williston, VT).
  • Chaichi M, Garcia-Rio E, Matsushita Y (2005) Curvature properties of four-dimensional Walker metrics. Classical Quantum Gravity 22:559-577.
  • Garcia-Rio E, Haze S, Katayama N, Matsushita Y (2008) Symplectic, Hermitian and Kahler structures on Walker 4-Manifolds. J. Geom. 90: 56-65.
  • S. I. Goldberg, Integrability of almost Kahler manifolds, Proc. Amer. Math. Soc. 21 (1969).
  • Matsushita Y, (2004) Four-dimensional Walker metrics and symplectic structure. J. Geom. Phys. 52: 89-99.
  • Matsushita Y, (2005) Walker 4-Manifolds with Proper Almost Complex Structure. J. Geom. Phys. 55: 385-398.
  • Nadjafikhah M, Jafari M (2013) Some general new Einstein Walker manifolds. Adv Math Phys, Art. ID 591852, 8 pp.
  • K. Sekigawa, On some compact Einstein almost Kahler manifolds, J. Math. Soc. Japan, 39 (1987), nˆA◦ 4, 677-684.
  • Walker AG (1950) Canonical form for a Riemannian space with a parallel field of null planes. Quart J Math Oxford 1(2): 69-79.
Year 2017, Volume: 5 Issue: 3, 253 - 261, 01.07.2017

Abstract

References

  • Banyaga A,Massamba F (2016) Non-existence of certain Einstein metrics on some symplectic manifolds, Forum Math 28(3):527- 537.
  • Brozos-Vazquez M, Garcia-Rio E, Gilkey P, Nikevic S, Vazquez-Lorenzo R (2009) The Geometry of Walker Manifolds. Synthesis Lectures on Mathematics and Statistics, 5. (Morgan and Claypool Publishers, Williston, VT).
  • Chaichi M, Garcia-Rio E, Matsushita Y (2005) Curvature properties of four-dimensional Walker metrics. Classical Quantum Gravity 22:559-577.
  • Garcia-Rio E, Haze S, Katayama N, Matsushita Y (2008) Symplectic, Hermitian and Kahler structures on Walker 4-Manifolds. J. Geom. 90: 56-65.
  • S. I. Goldberg, Integrability of almost Kahler manifolds, Proc. Amer. Math. Soc. 21 (1969).
  • Matsushita Y, (2004) Four-dimensional Walker metrics and symplectic structure. J. Geom. Phys. 52: 89-99.
  • Matsushita Y, (2005) Walker 4-Manifolds with Proper Almost Complex Structure. J. Geom. Phys. 55: 385-398.
  • Nadjafikhah M, Jafari M (2013) Some general new Einstein Walker manifolds. Adv Math Phys, Art. ID 591852, 8 pp.
  • K. Sekigawa, On some compact Einstein almost Kahler manifolds, J. Math. Soc. Japan, 39 (1987), nˆA◦ 4, 677-684.
  • Walker AG (1950) Canonical form for a Riemannian space with a parallel field of null planes. Quart J Math Oxford 1(2): 69-79.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Abdoul Salam Diallo

Fortune Massamba This is me

Publication Date July 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Diallo, A. S., & Massamba, F. (2017). Some properties of four-dimensional Walker manifolds. New Trends in Mathematical Sciences, 5(3), 253-261.
AMA Diallo AS, Massamba F. Some properties of four-dimensional Walker manifolds. New Trends in Mathematical Sciences. July 2017;5(3):253-261.
Chicago Diallo, Abdoul Salam, and Fortune Massamba. “Some Properties of Four-Dimensional Walker Manifolds”. New Trends in Mathematical Sciences 5, no. 3 (July 2017): 253-61.
EndNote Diallo AS, Massamba F (July 1, 2017) Some properties of four-dimensional Walker manifolds. New Trends in Mathematical Sciences 5 3 253–261.
IEEE A. S. Diallo and F. Massamba, “Some properties of four-dimensional Walker manifolds”, New Trends in Mathematical Sciences, vol. 5, no. 3, pp. 253–261, 2017.
ISNAD Diallo, Abdoul Salam - Massamba, Fortune. “Some Properties of Four-Dimensional Walker Manifolds”. New Trends in Mathematical Sciences 5/3 (July 2017), 253-261.
JAMA Diallo AS, Massamba F. Some properties of four-dimensional Walker manifolds. New Trends in Mathematical Sciences. 2017;5:253–261.
MLA Diallo, Abdoul Salam and Fortune Massamba. “Some Properties of Four-Dimensional Walker Manifolds”. New Trends in Mathematical Sciences, vol. 5, no. 3, 2017, pp. 253-61.
Vancouver Diallo AS, Massamba F. Some properties of four-dimensional Walker manifolds. New Trends in Mathematical Sciences. 2017;5(3):253-61.