We introduce the concept of a dynamical connection on a time-dependent Weil bundle and we characterize the structure of dynamical connections. Then we describe all torsions of dynamical connections.
A total connection of order in a Lie groupoid over is defined as a first order connections in the -st jet prolongations of . A connection in the groupoid together with a linear connection on its base, ie. in the groupoid , give rise to a total connection of order , which is called simple. It is shown that this simple connection is curvature-free iff the generating connections are. Also, an -th order total connection in defines a total reduction of the -th prolongation of to ....
[For the entire collection see Zbl 0699.00032.] A fibration is called totally noncohomologuous to zero (TNCZ) with respect to the coefficient field k, if is surjective. This is equivalent to saying that acts trivially on and the Serre spectral sequence collapses at . S. Halperin conjectured that for and F a 1-connected rationally elliptic space (i.e., both and are finite dimensional) such that vanishes in odd degrees, every fibration is TNCZ. The author proves this being the case...
For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that usual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.
We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension , and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on
We construct an analogue of Kontsevich and Vishik’s canonical trace for pseudodifferential boundary value problems in the Boutet de Monvel calculus on compact manifolds with boundary. For an operator in the calculus (of class zero), and an auxiliary operator , formed of the Dirichlet realization of a strongly elliptic second- order differential operator and an elliptic operator on the boundary, we consider the coefficient of in the asymptotic expansion of the resolvent trace (with large)...