curvature tensor

Also found in: Wikipedia.

curvature tensor

[′kər·və·chər ‚ten·sər]

(mathematics)

Mentioned in ?

References in periodicals archive ?

for any X, Y [member of] [GAMMA](TM), where S, Q and [GAMMA](TM) denote the Ricci curvature tensor, the Ricci operator with respect to the metric g and the Lie algebra of all vector fields on [M.

Yamabe solitons on three-dimensional Kenmotsu manifolds

The density [rho] is obtained from the curvature tensor of (1)

Repulsive gravity in the Oppenheimer-Snyder collapsar

alpha][beta]] of the curvature tensor of S, and the covariant of the third fundament form on S are then defined as follows (the explicit dependence on the variable y [member of] [bar.

Some Differential Geometric Relations in the Elastic Shell

It is well known that the structure of projective or KEnhler manifolds is governed by positivity or negativity properties of the curvature tensor.

ALKAGE: Algebraic and KEnhler geometry

n],) (n > 3) the curvature tensor R of type (0, 4) has the following form:

On Some Classes of Super Quasi-Einstein Manifolds

where S is the Ricci tensor of type (0, 2) and R is the curvature tensor of type (1 , 3).

Totally geodesic submanifolds of a trans-Sasakian manifold/ Taielikult geodeetilised trans-Sasaki muutkonna alammuutkonnad

His topics include the basics of geometry and relativity, affine connection and covariant derivative, the geodesic equation and its applications, curvature tensor and Einstein's equation, black holes, and cosmological models and the big bang theory.

Lectures on gravitation

If the curvature tensor R of the Riemannian manifold M satisfies

On hypersurfaces of semi-symmetric classes in a real space form

We denote by M(c), then the Riemannian curvature tensor of M(c) is given by

Semi-slant submanifolds of Kaehler product manifolds

n+2] and are a consequence of the Bianchi identities [1] for the curvature tensor.

Riemannian 4-spaces of class two

Synge's famous phrase, in General Relativity Theory the curvature tensor "is the gravitational field," then that body is not force-free since the curvature tensor cannot be made to vanish by a change of frames of reference.

What Spacetime Explains: Metaphysical Essays on Space and Time

As the shell becomes thicker, the contribution of Gauss curvature tensor in terms of energy is no more negligible as compared to that of the first two tensors used in classical thin shells.

Approximation of Linear Elastic Shells by Curved Triangular Finite Elements Based on Elastic Thick Shells Theory