We consider a Riemannian spin manifold (M, g) with a fixed spin structure. The zero sets of solutions of generalized Dirac equations on M play an important role in some questions arising in conformal spin geometry and in mathematical physics. In this setting the mass endomorphism has been defined as the constant term in an expansion of Green’s function for the Dirac operator. One is interested ...

We compare two approaches to Semi-Riemannian metrics of low regularity. The maximally “reasonable” distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombeau.

After recalling some background, we define Riemannian metrics and Riemannian manifolds. We analyze the basic tensorial operations that become available in the presence of a Riemannian metric. Then we construct the Levi-Civita connection, which is the basic " new " differential operator coming from such a metric. Background The purpose of this section is two–fold. On the one hand, we want to rel...

Abstract We propose a new axiom system for unitary quantum field theories on curved space-time backgrounds, by postulating that the partition function and correlators extend analytically to certain domain of complex-valued metrics. Ordinary Riemannian metrics are contained in allowable domain, while Lorentzian lie its boundary.

Let (M,g) be a compact Riemannian manifold. The conformal class of g consists of all metrics g̃ = e2ug for any smooth function u. A central theme in conformal geometry is the study of properties that are common to all metrics in the same conformal class, and the understanding and classification of all the conformal classes. For this purpose it is often useful to be able to single out a unique re...

We nd a Gaussian oo-diagonal heat kernel estimate for uniformly elliptic operators with measurable coeecients acting on regions R N , where the order 2m of the operator satisses N < 2m. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on. Work of Barbatis 1] is a...

We find a Gaussian off-diagonal heat kernel estimate for uniformly elliptic operators with measurable coefficients acting on regions Ω ⊆ R , where the order 2m of the operator satisfies N < 2m. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on Ω. Work of Barbat...

in this paper, we study a special class of generalized douglas-weyl metrics whose douglas curvature is constant along any finslerian geodesic. we prove that for every landsberg metric in this class of finsler metrics, ? = 0 if and only if h = 0. then we show that every finsler metric of non-zero isotropic flag curvature in this class of metrics is a riemannian if and only if ? = 0.

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Based on an idea of B. White [24], we prove an abstract genericity result that employs the infinite dimensional Sard–Smale theorem. Applications are given by proving the genericity of metric...

in this paper the general relatively isotropic l -curvature finsler metrics are studied. it isshown that on constant relatively landsberg spaces, the concepts of weakly landsbergian, landsbergianand generalized landsbergian metrics are equivalent. some necessary conditions for a relativelyisotropic l -curvature finsler metric to be a riemannian metric are also found.