Geodesic
Some results regarding an equation of Hamilton-Jacobi type
Archivum mathematicum, Tome 35 (1999) no. 3, pp. 203-214 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The main goal is to show that the pointwise Osserman four-dimensional pseudo-Riemannian manifolds (Lorentzian and manifolds of neutral signature $(--++)$) can be characterized as self dual (or anti-self dual) Einstein manifolds. Also, examples of pointwise Osserman manifolds which are not Osserman are discussed.
The main goal is to show that the pointwise Osserman four-dimensional pseudo-Riemannian manifolds (Lorentzian and manifolds of neutral signature $(--++)$) can be characterized as self dual (or anti-self dual) Einstein manifolds. Also, examples of pointwise Osserman manifolds which are not Osserman are discussed.
Classification : 35B10, 35B27, 35F20, 35R35, 80A25
Keywords: self-dual manifolds; manifolds of neutral signature; Jacobi operator; Einstein manifolds 
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     author = {Schmidt-Laine, C. and Edarh-Bossou, T. K.},
     title = {Some results regarding an equation of {Hamilton-Jacobi} type},
     journal = {Archivum mathematicum},
     pages = {203--214},
     year = {1999},
     volume = {35},
     number = {3},
     mrnumber = {1725838},
     zbl = {1046.35008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a1/}
}
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Schmidt-Laine, C.; Edarh-Bossou, T. K. Some results regarding an equation of Hamilton-Jacobi type. Archivum mathematicum, Tome 35 (1999) no. 3, pp. 203-214. http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a1/