Special homogeneous structures on Pseudo-Riemannian manifolds+
Special homogeneous structures on Pseudo-Riemannian manifolds+
The authors investigate homogeneous pseudo-Riemannian structures. They focus on a particular class of homogeneous structures named \textit{special}, and they show that all homogeneous structures on a compact orientable pseudo-Riemannian are special. Examples of such structures are the pseudo-Riemannian structures oft he class \(\mathcal T\)\(_2\oplus\mathcal T\)\(_3\), previously classified by \textit{P. M. Gadea} and \textit{J. A. Oubina} [Monatsh. Math. 124, No.~1, 17--34 (1997; Zbl 0901.53036)]. They also consider Lorenzian homogeneous structures on three-dimensional Lorentzian Lie groups. They show that all unimodular such Lie groups admit a Lorentzian homogeneous structure of the class \(\mathcal T\)\(_2\oplus\mathcal T\)\(_3\). For the non-unimodular case, it is shown that each three-dimensional Lorentzian non-unimodular Lie group satisfying an additional condition, admits a Lorentzian homogeneous structure of the class \(\mathcal T\)\(_1\oplus\mathcal T\)\(_2\) or of the class \(\mathcal T\)\(_1\oplus\mathcal T\)\(_3\).
- University of Salento Italy
Lorentz homogeneous structure, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Differential geometry of homogeneous manifolds, Geodesics in global differential geometry, pseudo-Riemannian homogeneous structures, pseudo-Riemannian homogeneous space, homogeneous structure
Lorentz homogeneous structure, Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics, Differential geometry of homogeneous manifolds, Geodesics in global differential geometry, pseudo-Riemannian homogeneous structures, pseudo-Riemannian homogeneous space, homogeneous structure
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