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Normal holonomy groups and $$s$$-representations. (English) Zbl 0759.53034
The normal holonomy group representation of a submanifold of Euclidean space is, up to a trivial factor, equivalent to an $$s$$-representation (i.e. isotropy representation of a semisimple symmetric space). By computing the normal holonomy groups of the (focal) orbits of the $$s$$- representations we show conversely that almost every of these representations do occur as normal holonomy representations.

##### MSC:
 53C40 Global submanifolds 53C35 Differential geometry of symmetric spaces
##### Keywords:
focal orbits; isotropy representation
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