Submanifolds and holonomy Sergio Console General setup: Reduction of codim Moore’s lemma Normal holonomy TOOLS: METHOD: Focalization Holonomy tube Model spaces (submanifolds with constant principal curvatures or orbits of s-representations)

Holonomy and curvature

There are no parallel tensor fields (normal) except those coming from the metric

It has non positive scalar curvature normal holonomy is non exceptional use (a part of) Simons’ proof of Berger Theorem

Complex projective space Full flags

For isoparametric submanifolds