On decomposition of generalized Riemannian symmetric spaces and complete lifts of Clifford translations
Tóm tắt
Kowalski (Generalized symmetric spaces, Springer, 1980), proved that for Riemannian manifolds
$$M_1$$
and
$$M_2$$
, if their Riemannian direct product
$$M={{M}_{1}}\times {{M}_{2}}$$
is Riemannian symmetric spaces, then
$$M_1$$
and
$$M_2$$
are Riemannian symmetric spaces. This paper examines this theorem in generalized symmetric spaces, without assuming that each
$$M_i$$
is simply connected.
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