‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

Let $(g, X)$ be a K\"ahler-Ricci soliton on complex manifold $M$. We prove that if the K\"ahler $(M, g)$ can immersed into definite or indefinite space form of constant holomorphic sectional curvature $2c$, then $g$ is Einstein. Moreover, its Einstein rational multiple $c$.

Two-point functions for scalar and spinor fields are investigated in Einstein universe (R ⊗ S). Equations for massive scalar and spinor two-point functions are solved and the explicit expressions for the two-point functions are given. The simpler expressions for massless cases are obtained both for the scalar and spinor cases. e-mail : [email protected] e-mail : ishikawa@t...

Starting from a real analytic surface ℳ with conformal Cartan connection A. Bor´owka constructed minitwistor space of an asymptotically hyperbolic Einstein–Weyl manifold being the boundary. In this article, starting symmetry connection, we prove that symmetries on can be extended to obtained manifold.

Let M = G/K be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group G. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume. 2000 Mathematics Subject Classification. Pr...

After analyzing renormalization schemes on a Poincaré-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior under a variation of the Poincaré-Einstein structure, and obtain, from the renor...

TIn this article, the M-projective and Weyl curvature tensors on a normal paracontact metric manifold are discussed. For manifolds, pseudosymmetric cases investigated some interesting results obtained. We show that semisymmetric is of constant sectional curvature. also obtain an $\eta$-Einstein manifold. Finally, we support our topic with example.

Let (M, g) be a compact Einstein manifold with smooth boundary. Let ∆p,B be the realization of the p form valued Laplacian with a suitable boundary condition B. Let Spec(∆p,B) be the spectrum where each eigenvalue is repeated according to multiplicity. We show that certain geometric properties of the boundary may be spectrally characterized in terms of this data where we fix the Einstein constant.

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold M admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics η on M × R such that (M × R, η) admit Einstein spinors (resp. weak Killing spinors). To prove the result we split the Einstein-Dirac equ...

Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M = M 0 × n i=1 M i (n ≥ 1) are investigated under dimensional reduction to a D 0-dimensional effective non-minimally coupled σ-model which generalizes the familiar Brans-Dicke model. It is argued that the Einstein frame should be considered as the physical one. The general prescription for the Eins...