Scalar curvature
Scalar curvature In Riemannian geometry, the scalar curvature (or Ricci scalar) is the simplest way of describing ...
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Talk:Scalar curvature
Talk:Scalar curvature Notation -- R vs S I originally switched ... other article on WP that talks about scalar curvature uses R not S (since S is ... yet to see any book where the scalar curvature is denoted by S. Neither ...
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Curvature
Curvature Curvature refers to a number of loosely related ... concepts in different areas of geometry. Intuitively, Curvature is the amount by which a geometric ... There is a key distinction between extrinsic curvature which is defined for objects embedded in ... way that relates to the radius of curvature of circles that touch the object, ...
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Kretschmann scalar
Kretschmann scalar In the theory of Lorentzian manifolds, particularly ... of applications to general relativity, the Kretschmann scalar is a quadratic scalar invariant. It was introduced by Ernst Kretschmann ... math>R_{abcd} is the Riemann curvature tensor. Because it is a sum of ... math> is the Weyl tensor, the conformal curvature tensor which is also the completely ...
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Curvature invariant
Curvature invariant This article is in need of ... In Riemannian geometry and pseudo-Riemannian geometry , curvature invariants are scalar quantities constructed from Riemann tensors using contractions ... constructed in the same way. Types of curvature invariants The invariants most often considered are ... whose coefficients and roots (eigenvalues) are polynomial scalar invariants. Physical applications In metric theories ...
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Scalar wave   (translated from German)
Scalar wave Scalar waves are hypothetical Waves , itself of the ... however so far one did not prove. Scalar waves become also as electromagnetic Longitudinal waves ... designated. Table of contents Theses of the scalar wave model From the established science recognized theses The scalar wave model for that Vacuum none ...
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Scalar field
Scalar field In mathematics and physics, a scalar field associates a scalar to every point in space. Scalar fields are often used in physics, for ... space, or the air pressure. Definition A scalar field is a function from R ...
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Constant curvature
Constant curvature In mathematics, constant curvature in differential geometry is a concept most ... commonly applied to surfaces. For those the scalar curvature is a single number determining the local ... at all points. The circle has constant curvature, also, in a natural (but different) ...
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Geodesic curvature
Geodesic curvature In differential geometry, the geodesic curvature vector is a property of curves in ... P on a curve C, the geodesic curvature vector k g is the curvature vector k of the projection of the ... onto the tangent plane at P. The scalar magnitude of the geodesic curvature vector ...
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Ricci curvature
Ricci curvature It has been suggested that Trace-free ... section. (Discuss) In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is ... obtained as a trace of the full curvature tensor. It can be thought of as ... u where R is the Riemann curvature tensor. In local coordinates, one can write ... is the only independent trace of the curvature tensor; all others vanish or are ...
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