Flat Homogeneous Pseudo-Riemannian Manifolds
نویسنده
چکیده
The complete homogeneous pseudo-Riemannian manifolds of constant non-zero curvature were classified up to isometry in 1961 [1]. In the same year, a structure theory [2] was developed for complete fiat homogeneous pseudo-Riemannian manifolds. Here that structure theory is sharpened to a classification. This completes the classification of complete homogeneous pseudo-Riemannian manifolds of arbitrary constant curvature. Mathematics Subject Classifications: Primary, 53C30, 53C50; Secondary, 14H30.
منابع مشابه
Isoclinic Spheres and Flat Homogeneous Pseudo - Riemannian Manifolds
The structure theory ([3], [8]) for complete flat homogeneous pseudo-riemannian manifolds reduces the classification to the solution of some systems of quadratic equations. There is no general theory for that, but new solutions are found here by essentially the same construction as that used for isoclinic spheres in Grassmann manifolds [4]. It is interesting to speculate on a possible direct ge...
متن کاملCurvature Homogeneous Pseudo-riemannian Manifolds Which Are Not Locally Homogeneous
We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.
متن کاملCommutative curvature operators over four-dimensional generalized symmetric spaces
Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.
متن کامل. D G ] 1 6 O ct 2 00 4 NON - REDUCTIVE HOMOGENEOUS PSEUDO - RIEMANNIAN MANIFOLDS OF DIMENSION FOUR
A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...
متن کامل. D G ] 8 J un 2 00 4 NON - REDUCTIVE HOMOGENEOUS PSEUDO - RIEMANNIAN MANIFOLDS OF DIMENSION FOUR
A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...
متن کامل