Sabinin‘s method for classification of local Bol loops
Séances de problèmes
Singleton representations of
Some invariants of Lie algebroids of principal fibre bundles
Some special geometry in dimension six
Motivated by the study of CR-submanifolds of codimension in , the authors consider here a -dimensional oriented manifold equipped with a -dimensional distribution. Under some non-degeneracy condition, two different geometric situations can occur. In the elliptic case, one constructs a canonical almost complex structure on ; the hyperbolic case leads to a canonical almost product structure. In both cases the only local invariants are given by the obstructions to integrability for these structures....
Some theorems for holomorphic functions with proximate order
Space-time decompositions via differential forms
The author presents a simple method (by using the standard theory of connections on principle bundles) of -decomposition of the physical equations written in terms of differential forms on a 4-dimensional spacetime of general relativity, with respect to a general observer. Finally, the author suggests possible applications of such a decomposition to the Maxwell theory.
Spectral theory of invariant operators, sharp inequalities, and representation theory
The paper represents the lectures given by the author at the 16th Winter School on Geometry and Physics, Srni, Czech Republic, January 13-20, 1996. He develops in an elegant manner the theory of conformal covariants and the theory of functional determinant which is canonically associated to an elliptic operator on a compact pseudo-Riemannian manifold. The presentation is excellently realized with a lot of details, examples and open problems.
Spingroups and spherical means III
Spinor equations in Weyl geometry
This paper deals with Dirac, twistor and Killing equations on Weyl manifolds with -spin structures. A conformal Schrödinger-Lichnerowicz formula is presented and used to derive integrability conditions for these equations. It is shown that the only non-closed Weyl manifolds of dimension greater than 3 that admit solutions of the real Killing equation are 4-dimensional and non-compact. Any Weyl manifold of dimension greater than 3, that admits a real Killing spinor has to be Einstein-Weyl.
Square integrability of group representations on homogeneous spaces and generalized coherent states
Supersymmetry, a biased review
In spite of the provocative title this is a run of the mill review of supersymmetry. The only thing which deserves some comment is that the author seems to think that coordinate free and coordinate dependent treatments belong to conflicting cultures. This is definitely not true. Coordinate free treatments concentrate one's mind on the geometry while coordinate dependent treatments are indispensable for computations producing numbers which can be compared with experimental values. Those who use the...
Symmetric algebras and Yang-Baxter equation
Let be an open subset of the complex plane, and let denote a finite-dimensional complex simple Lie algebra. A. A. Belavin and V. G. Drinfel’d investigated non-degenerate meromorphic functions from into which are solutions of the classical Yang-Baxter equation [Funct. Anal. Appl. 16, 159-180 (1983; Zbl 0504.22016)]. They found that (up to equivalence) the solutions depend only on the difference of the two variables and that their set of poles forms a discrete (additive) subgroup of the...
Symplectic solution supermanifolds in field theory
Summary: For a large class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold of classical solutions in Minkowski space can be constructed. This solution supermanifold carries a natural symplectic structure; the resulting Poisson brackets between the field strengths are the classical prototypes of the canonical (anti-) commutation relations. Moreover, we discuss symmetries and the Noether theorem in this context.