Curvature structures and conformal transformations

Curvature Structures and Conformal Transformations

1. The notion of a "curvature structure" was introduced in §8, Chapter 1 of [ l ] . In this note we shall consider some of its applications. The details will be presented elsewhere. Let (M, g) be a Riemann manifold. Whenever convenient, we shall denote the inner product defined by g, by ( ). DEFINITION. A curvature structure on (M, g) is a (1, 3) tensor field T such that, for any vector fields ...

Spacetimes admitting quasi-conformal curvature tensor

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

Conformal Structures and Necksizes of Embedded Constant Mean Curvature Surfaces

Let M = Mg,k denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with k (labeled) ends, modulo rigid motions, endowed with the real analytic structure described in [15]. Let P = Pg,k = Rg,k × R+ be the space of parabolic structures over Riemann surfaces of genus g with k (marked) punctures, the real analytic structure coming from the 3g− 3+ k loc...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

2.1.1 Conformal Transformations......................... 6