Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the...

We present a model in which the breackdown of conformal symmetry of a quantum stress-tensor due to the trace anomaly is related to a cosmological effect in a gravitational model. This is done by characterizing the traceless part of the quantum stress-tensor in terms of the stress-tensor of a conformal invariant classical scalar field. We introduce a conformal frame in which the anomalous trace ...

We investigate the Wightman function, the vacuum expectation values of the field squared and the energy-momentum tensor for a massless scalar field with general curvature coupling parameter in spatially flat Friedmann-Robertson-Walker universes with an arbitrary number of toroidally compactified dimensions. The topological parts in the expectation values are explicitly extracted and in this way...

We generalize the Quantum Geometric Tensor by replacing a Hamiltonian with modular Hamiltonian. The symmetric part of provides Fubini-Study metric, and its anti-symmetric sector gives Berry curvature. Our generalization dubbed Modular metric curvature Kinematic Space. also use result identity Virasoro block to relate connected correlator two Wilson lines two-point function This relation realize...

Abstract We study conformal $$\eta$$ ? -Einstein solitons on the framework of trans-Sasakian manifold in dimension three. Existence is discussed. Then we find some results which are where Ricci tensor cyclic parallel and Codazzi type. also consider curvature conditions with addition to manifold. use torse-for...

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...

We show that the recently developed pseudoparticle operator algebra which generates the low-energy Hamiltonian eigenstates of multicomponent integrable systems also provides a natural operator representation for the the Virasoro algebras associated with the conformal-invariant character of the low-energy spectrum of the these models. Studying explicitly the Hubbard chain in a non-zero chemical ...

Let D be a proper subdomain of R" and kD the quasihyperbolic metric defined by the conformal metric tensor ds2 = dist(x, dD)~2ds2. The geodesies for this and related metrics are shown, by purely geometric methods, to exist and have Lipschitz continuous first derivatives. This is sharp for kD; we also obtain sharp estimates for the euclidean curvature of such geodesies. We then use these results...