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# Allen Henry Back

Assistant Professor

## 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

(2000).*Inverting*a Batting Average - an Application of Continued Fractions*(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.