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# Allen Back

Senior Lecturer (Retired)

## Overview

### Research Focus

- Differential Geometry
- Curvature Realizability
- Einstein Metrics
- Positive Ricci Curvature on Cohomogeniety one Manifolds
- Equivariant Differential Geometry
- Transformation Groups
- Homotopy Theory
- Dynamical Systems
- Mathematical Physics
- Geometric Modeling and Robotics

### Departments/Programs

- Mathematics

## Publications

Inverting a Batting Average - an Application of Continued Fractions (2000). (A small observation perhaps obvious to anyone who knows the theory of continued fractions.)

Mathematics and Tensegrity (with Robert Connelly) American Scientist , Volume 86 (1998) 142-151.

From Instantaneous Motion to Task-Directed Constrained Manipulation (with Daniela Rus) IEEE Intelligent Robots and Systems Volume 3 (1993) 1598 - 1605.

dstool: Computer Assisted Exploration of Dynamical Systems (with J. Guckenheimer, M. Myers, F.J. Wicklin, and P. Worfolk), Notices of the American Mathematical Society 39 (1992) 303 - 309.

A Dynamical Simulation Facility for Hybrid Systems (1992) (with John Guckenheimer and Mark Myers), in Lecture Notes in Computer Science 736, Hybrid Systems edited by Robert L. Grossamn, et. al., Springer Verlag, Berlin, 1993.

Systematic Conversion of Boundary Integral Surface Integrals to Contour Integrals (1992), (with E.D.Lutz, L.G.Gray, and A.R.Ingraffea), Cornell Department of Civil And Environmental Engineering Report 92-6.

Solid Quality Norms and Consistency Strategies in Robust Intersection of Simplicial Complexes (1990).

Local Theory of Equivariant Einstein Metrics and Ricci Realizability on Kervaire Spheres (1986).

Kervaire Spheres and Equivariant Geometry (with Wu - Yi Hsiang), Transactions American Mathematical Society 304 (1987) 207 - 227. JSTOR Version

Fundamental Equations in Equivariant Geometry (with Manfredo do Carmo and Wu - Yi Hsiang) (1984).

Pontryagin Forms on Homogeneous Spaces, Commentari Mathematica Helvetica 57 (1982) 349 - 355. GDZ persistent URL

Rational Pontryagin Classes and Killing Forms, Journal of Differential Geometry 16 (1981) 191 - 193. JDG Archive Version

Homotopy Rigidity For Grassmanians, Proceedings American Mathematical Society 80 (1980) 327 - 332. JSTOR Version

New Gravitational Instantons and Universal Spin Structures (with P. Freund and M. Forger), Physics Letters 77B (1978) 181 - 184.

Involutions on Grassman Manifolds, Ph. D. Thesis, Berkeley 1977.