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Traceless component of the conformal curvature tensor in Kähler manifold

Shoichi Funabashi, Hyang Sook Kim, Y.-M. Kim, Jin Suk Pak (2006)

Czechoslovak Mathematical Journal

We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension 4 , 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 p ...

Traces and quasi-traces on the Boutet de Monvel algebra

Gerd Grubb, Elmar Schrohe (2004)

Annales de l’institut Fourier

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 A in the calculus (of class zero), and an auxiliary operator B , formed of the Dirichlet realization of a strongly elliptic second- order differential operator and an elliptic operator on the boundary, we consider the coefficient C 0 ( A , B ) of ( - λ ) - N in the asymptotic expansion of the resolvent trace Tr ( A ( B - λ ) - N ) (with N large)...

Transition operators on co-compact G-spaces.

Laurent Saloff-Coste, Wolfgang Woess (2006)

Revista Matemática Iberoamericana

We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with respect to the group orbits. We then introduce reduced transition operators on the compact factor space whose norms and spectral radii are upper bounds for the Lp-norms and spectral radii of the original operator. If the group is amenable then the spectral radii of the original and reduced operators coincide,...

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