Addendum to "Ricci-flat holonomy: a Classification": the case of Spin(10)

TL;DR

This paper completes the classification of Ricci-flat holonomy algebras by analyzing specific subalgebras related to Spin(10), confirming they are of Ricci-type.

Contribution

It extends previous work by classifying irreducible holonomy algebras related to Spin(10) as Ricci-type, filling a gap in the earlier classification.

Findings

All considered subalgebras are of Ricci-type.

Provides a complete classification for the Spin(10) case.

Fills a gap in the previous Ricci-flat holonomy classification.

Abstract

This note fills a hole in the author's previous paper ``Ricci-Flat Holonomy: a Classification'', by dealing with irreducible holonomy algebras that are subalgebras or real forms of $\mbb{C} \oplus \mf{spin}(10,\mbb{C})$. These all turn out to be of Ricci-type.