Also, you might want to look at the list of my earlier writings.
This is the text of a lecture that I gave at the Institut d'Élie Cartan in Nancy, France in June 1998 as part of their Journées d'Élie Cartan.
The theme is that Cartan's understanding of the role of duality in the homogeneous spaces of the rank 2 Lie groups had a profound effect on his development of the method of equivalence, connections, path geometry, and so on.
This is supposed to be published by the IECN at some point in their in-house series containing the proceedings of the Journées.
Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivial can be isometrically embedded as a coassociative submanifold in a G_2-manifold, even as the fixed locus of an anti-G_2 involution.
These results, when coupled with McLean's analysis of the moduli spaces of such calibrated submanifolds, yield a plentiful supply of examples of compact calibrated submanifolds with nontrivial deformation spaces.
In this article, I classify the hypersurfaces described in the title. The interesting thing is that it turns out that nearly all of the solutions are invariant under a 1-parameter group of isometries. The one exception (up to holomorphic homothety) is a certain hypersurface in C^2 with very interesting properties. Though it has no continuous symmetries, it is periodic with respect to a lattice of type F_4 and the complex leaves in the lattice quotient are compact Riemann surfaces of genus 3.
This is a set of notes on the action of certain spin groups on their spinor spaces, mostly concentrating on the 'medium low' dimensions, Spin(p,q) where (p,q) is one of (8,0), (9,0), (10,0), (9,1), (11,0), (10,1), and (10,2).
I wrote these in preparation for doing some work on constructing examples of pseudo-Riemannian manifolds of type (10,1) that have a parallel spinor of algebraically special type. (I needed a treatment of the spinors in these dimensions that used a consistent notation.)
Nothing in these notes is new. I am making them available because they have been referred to in the literature and I have been receiving requests for them.
This is a short remark giving a local description of the metrics in 10+1 dimensions that possess a parallel null spinor and have the maximal degree of holonomy among such metrics. I show that the holonomy can be as large as is allowed by the existence of a parallel spinor. There is an interesting relation with Spin(7)-metrics (actually 1-parameter families of such) in the solution.
This is a longer, more expository version of the published manuscript Finsler structures on the 2-sphere satisfying K=1. I do not plan to submit it for publication, but will instead incorporate it into my Aisenstadt lectures.
I may not submit this for publication, but instead incorporate it into my Aisenstadt lectures.