Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem"

Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of Karpelevich-Mostow theorem. We also include a short discussion of the original proof by Karpelevich

Mok's characteristic varieties and the normal holonomy group

In this paper we complete the study of the normal holonomy groups of complex submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non transitive normal holonomies are exactly the Hermitian s-representations of [CD09, Table 1] (see Corollary 1.1). For each one of them we construct a non necessarily complete complex submanifold whose normal holonomy is the prescribed s-representation. We also show that if the submanifold has irreducible non transitive normal holonomy then it is an open subset of the smooth part of one of the characteristic varieties studied by N. Mok in his work about rigidity of locally symmetric spaces. Finally, we prove that if the action of the normal holonomy group of a projective submanifold is reducible then the submanifold is an open subset of the smooth part of a so called join, i.e. the union of the lines joining two projective submanifolds

A geometric proof of the Karpelevich-Mostow's theorem

In this paper we give a geometric proof of the Karpelevich's theorem that asserts that a semisimple Lie subgroup of isometries, of a symmetric space of non compact type, has a totally geodesic orbit. In fact, this is equivalent to a well-known result of Mostow about existence of compatible Cartan decompositions

Intrinsic palindromic numbers

We introduce a notion of palindromicity of a natural number which is independent of the base. We study the existence and density of palindromic and multiple palindromic numbers, and we raise several related questions.Comment: 6 pages, Latex2