Now showing items 1-8 of 8

• #### A circle quotient of a $G_2$ cone ﻿

A study is made of $R^6$ as a singular quotient of the conical space $R^+\times CP^3$ with holonomy $G_2$ with respect to an obvious action by $U(1)$ on $CP^3$ with fixed points. Closed expressions are found for the induced ...
• #### Harmonic morphisms with fibers of dimension one ﻿

(Communications in Analysis and Geometry, 2000-04-01)
The harmonic morphisms φ : Mn+1 → Nn are studied using the methods of the moving frame and exterior differential systems and three main results are achieved. The first result is a local structure theorem for such maps in ...
• #### Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms ﻿

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is ...
• #### Notes on spinors in low dimension ﻿

The purpose of these old notes (written in 1998 during a research project on holonomy of pseudo-Riemannian manifolds of type (10,1)) is to determine the orbit structure of the groups Spin(p,q) acting on their spinor spaces ...
• #### Recent Advances in the Theory of Holonomy ﻿

This article is a report on the status of the problem of classifying the irriducibly acting subgroups of GL(n,R) that can appear as the holonomy of a torsion-free affine connection. In particular, it contains an account ...
• #### Remarks on the geometry of almost complex 6-manifolds ﻿

This article is mostly a writeup of two talks, the first given in the Besse Seminar at the Ecole Polytechnique in 1998 and the second given at the 2000 International Congress on Differential Geometry in memory of Alfred ...
• #### Second order families of special Lagrangian 3-folds ﻿

A second order family of special Lagrangian submanifolds of complex m-space is a family characterized by the satisfaction of a set of pointwise conditions on the second fundamental form. For example, the set of ruled special ...
• #### Some remarks on Finsler manifolds with constant flag curvature ﻿

(Houston Journal of Mathematics, 2002)
This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. The first remark is that there is a canonical Kahler structure on the space of geodesics ...