![]() If the Weyl tensor vanishes in dimension ≥ 4, then the metric is locally conformally flat: there exists a local coordinate system in which the metric tensor is proportional to a constant tensor. In dimensions ≥ 4, the Weyl curvature is generally nonzero. In dimensions 2 and 3 the Weyl curvature tensor vanishes identically. More generally, the Weyl curvature is the only component of curvature for Ricci-flat manifolds and always governs the characteristics of the field equations of an Einstein manifold. In general relativity, the Weyl curvature is the only part of the curvature that exists in free space-a solution of the vacuum Einstein equation-and it governs the propagation of gravitational waves through regions of space devoid of matter. It is obtained from the Riemann tensor by subtracting a tensor that is a linear expression in the Ricci tensor. This tensor has the same symmetries as the Riemann tensor, but satisfies the extra condition that it is trace-free: metric contraction on any pair of indices yields zero. ![]() The Ricci curvature, or trace component of the Riemann tensor contains precisely the information about how volumes change in the presence of tidal forces, so the Weyl tensor is the traceless component of the Riemann tensor. The Weyl tensor differs from the Riemann curvature tensor in that it does not convey information on how the volume of the body changes, but rather only how the shape of the body is distorted by the tidal force. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. You may be contacted on behalf of the NHS to confirm any details you have provided.Measure of the curvature of a pseudo-Riemannian manifold hospitals) and NHS Digital, for the purposes of validation, invoicing and cost recovery. The information you give on this form will be used to assist in identifying your chargeable status, and may be shared, including with NHS secondary care organisations (e.g. ![]() Even if you have to pay for a service, you will always be provided with any immediately necessary or urgent treatment, regardless of advance payment. You may be asked to provide proof of entitlement in order to receive free NHS treatment outside of the GP practice, otherwise you may be charged for your treatment. More information on ordinary residence, exemptions and paying for NHS services can be found in the Visitor and Migrant patient leaflet, available from your GP practice. Some services, such as diagnostic tests of suspected infectious diseases and any treatment of those diseases are free of charge to all people, while some groups who are not ordinarily resident here are exempt from all treatment charges. In most cases, nationals of countries outside the European Economic Area must also have the status of 'indefinite leave to remain' in the UK. Being ordinarily resident broadly means living lawfully in the UK on a properly settled basis for the time being. However, if you are not 'ordinarily resident' in the UK you may have to pay for NHS treatment outside of the GP practice. Anybody in England can register with a GP practice and receive free medical care from that practice.
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