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Transactions of the American Mathematical Society

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Classification of simply connected four-dimensional $ RR$-manifolds

Authors: Gr. Tsagas and A. Ledger
Journal: Trans. Amer. Math. Soc. 219 (1976), 189-210
MSC: Primary 53C30
MathSciNet review: 0467603
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Abstract: Let (M, g) be a Riemannian manifold. We assume that there is a mapping $ s:M \to I(M)$, where $ I(M)$ is the group of isometries of (M, g), such that $ {s_x} = s(x),\forall x \in M$, has x as a fixed isolated point, then (M, g) is called a Riemannian s-manifold. If the tensor field S on M defined by the relation $ {S_x} = {(d{s_x})_x},\forall x \in M$, is differentiable and invariant by each isometry $ {s_x}$, then the manifold (M, g) is called a regularly s-symmetric Riemannian manifold. The aim of the present paper is to classify simply connected four-dimensional regularly s-symmetric Riemannian manifolds.

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Keywords: Simply connected manifold, Lie group, Lie algebra, s-structure, Riemannian s-manifold, symmetry tensor field, symmetric space, adjoint group
Article copyright: © Copyright 1976 American Mathematical Society