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A class of metrics on tangent bundles of pseudo-Riemannian manifolds

H. M. Dida, A. Ikemakhen (2011)

Archivum Mathematicum

We provide the tangent bundle T M of pseudo-Riemannian manifold ( M , g ) with the Sasaki metric g s and the neutral metric g n . First we show that the holonomy group H s of ( T M , g s ) contains the one of ( M , g ) . What allows us to show that if ( T M , g s ) is indecomposable reducible, then the basis manifold ( M , g ) is also indecomposable-reducible. We determine completely the holonomy group of ( T M , g n ) according to the one of ( M , g ) . Secondly we found conditions on the base manifold under which ( T M , g s ) ( respectively ( T M , g n ) ) is Kählerian, locally symmetric or Einstein...

A classification of certain submanifolds of an S-manifold

José L. Cabrerizo, Luis M. Fernández, Manuel Fernández (1991)

Annales Polonici Mathematici

A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.

A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

Oldřich Kowalski, Barbara Opozda, Zdeněk Vlášek (2004)

Open Mathematics

The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].

A classification of Poisson homogeneous spaces of complex reductive Poisson-Lie groups

Eugene Karolinsky (2000)

Banach Center Publications

Let G be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous G-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence between Poisson homogeneous G-spaces and Lagrangian subalgebras in the double D𝖌 (here 𝖌 = Lie G). A geometric interpretation of some Poisson homogeneous G-spaces is also proposed.

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