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- W1988033135 abstract "A Walker n-manifold is a semi-Riemannian manifold, which admits a field of parallel null r-planes, with . In the present paper we study curvature properties of a Walker 4-manifold (M, g) which admits a field of parallel null 2-planes. The metric g is necessarily of neutral signature (+ + − −). Such a Walker 4-manifold is the lowest dimensional example not of Lorentz type. There are three functions of coordinates which define a Walker metric. Some recent work shows that a Walker 4-manifold of restricted type whose metric is characterized by two functions exhibits a large variety of symplectic structures, Hermitian structures, Kähler structures, etc. For such a restricted Walker 4-manifold, we shall study mainly curvature properties, e.g., conditions for a Walker metric to be Einstein, Osserman, or locally conformally flat, etc. One of our main results is the exact solutions to the Einstein equations for a restricted Walker 4-manifold." @default.
- W1988033135 created "2016-06-24" @default.
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- W1988033135 date "2005-01-19" @default.
- W1988033135 modified "2023-10-18" @default.
- W1988033135 title "Curvature properties of four-dimensional Walker metrics" @default.
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- W1988033135 doi "https://doi.org/10.1088/0264-9381/22/3/008" @default.
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