Extrinsic homogeneity of parallel submanifolds. II
Let \(N\) be a Riemannian symmetric space and \(f:M\rightarrow N\) an isometric immersion. Let \(TM\), \(\bot f\), \(h:TM\times TM\rightarrow \bot f\) and \(S:TM\times \bot f\rightarrow TM\) denote the tangent bundle of \(M\), the normal bundle of \(f\), the second fundamental form and the shape operator, respectively. In the vector bundle \(B\) of \(\bot f\)-valued symmetric bilinear forms on \(M\), there is a distinguished element, namely \(h\). Then \(f\) or \(M\) are called parallel if \(h\) is a parallel section of \(B\). The paper under review gives very interesting answers to the question, whether there exists a subgroup of isometries of \(N\) which acts transitively on a parallel \(M\). A main hypothesis is that the universal covering space of \(M\) has no Euclidean factor. [For Part I see Ann. Global Anal. Geom. 38, No. 4, 335--371 (2010; Zbl 1206.53055).]
scientific article; zbMATH DE number 5880284