The purpose of this paper is to study the convergence problem of Mann and Ishikawa type iterative schemes of weakly contractive mapping in a complete convex metric space. We establish the results on invariant approximation for the mapping defined on a class of nonconvex sets in a convex metric space. Finally, we obtain the existence of common fixed points of two asymptotically nonexpansive mapp...

We present a proof of a conjecture of Deser and Schwimmer regarding the algebraic structure of “global conformal invariants”; these are defined to be scalar quantities whose integrals over compact manifolds remain invariant under conformal changes of the underlying metric. We prove that any such invariant can be expressed as a linear combination of a local conformal invariant, a divergence, and...

Visually recognizing objects at different orientations and distances has been assumed to depend either on extracting from the retinal image a viewpoint-invariant, typically three-dimensional (3D) structure, such as object parts, or on mentally transforming two-dimensional (2D) views. To test how these processes might interact with each other, an experiment was performed in which observers discr...

We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations both gravitational field and particle's position around flat space. Using recent relational approach construct gauge-invariant observables, we compute one-loop graviton corrections invariant metric perturbation, whose time-time component gives Newtonian potential. The resulting ...

The global holomorphic invariant αG(M) introduced by Tian[6], Tian and Yau[5] is closely related to the existence of Kähler-Einstein metrics. In his solution of the Calabi conjecture, Yau[11] proved the existence of a KählerEinstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is positiv...

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric positive scalar curvature.