1. CJM 2008 (vol 60 pp. 1336)
|Moving Frames for Lie Pseudo--Groups |
We propose a new, constructive theory of moving frames for Lie pseudo-group actions on submanifolds. The moving frame provides an effective means for determining complete systems of differential invariants and invariant differential forms, classifying their syzygies and recurrence relations, and solving equivalence and symmetry problems arising in a broad range of applications.
Categories:58A15, 58A20, 58H05, 58J70
2. CJM 2005 (vol 57 pp. 99)
|Second Order Operators on a Compact Lie Group |
We describe the structure of the space of second order elliptic differential operators on a homogenous bundle over a compact Lie group. Subject to a technical condition, these operators are homotopic to the Laplacian. The technical condition is further investigated, with examples given where it holds and others where it does not. Since many spectral invariants are also homotopy invariants, these results provide information about the invariants of these operators.
3. CJM 2004 (vol 56 pp. 638)
|Multisymplectic Reduction for Proper Actions |
We consider symmetries of the Dedonder equation arising from variational problems with partial derivatives. Assuming a proper action of the symmetry group, we identify a set of reduced equations on an open dense subset of the domain of definition of the fields under consideration. By continuity, the Dedonder equation is satisfied whenever the reduced equations are satisfied.
Keywords:Dedonder equation, multisymplectic structure, reduction,, symmetries, variational problems