Some properties of four-dimensional Walker manifolds

ISSN: 2147-5520
Başlangıç: 2015
Yayıncı: Biska Bilişim

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

Keywords:

Einstein metric, locally symmetry locally conformally flat, Walker metrics,

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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.