An inequality between intrinsic and extrinsic scalar curvature invariants for codimension 2 embeddings

2004 ◽  
Vol 52 (2) ◽  
pp. 101-112 ◽  
Author(s):  
Franki Dillen ◽  
Stefan Haesen ◽  
Miroslava Petrović-Torgašev ◽  
Leopold Verstraelen
Keyword(s):  
Scalar Curvature ◽  
Curvature Invariants

SCALAR AVERAGING IN COSMOLOGY

2010 ◽  
Vol 19 (14) ◽  
pp. 2361-2364
Author(s):  
A. A. COLEY
Keyword(s):  
Scalar Curvature ◽  
Cosmological Evolution ◽  
Considerable Importance ◽  
Correct Interpretation ◽  
Curvature Invariants ◽  
Averaging Problem ◽  
Cosmological Data

The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. In this essay an approach to averaging based on scalar curvature invariants is presented, which gives rise to significant effects on cosmological evolution.

scholarly journals Basis for scalar curvature invariants in three dimensions

2014 ◽  
Vol 31 (23) ◽  
pp. 235010 ◽  
Author(s):  
A A Coley ◽  
A MacDougall ◽  
D D McNutt
Keyword(s):  
Scalar Curvature ◽  
Three Dimensions ◽  
Curvature Invariants

scholarly journals Curvature operators and scalar curvature invariants

2010 ◽  
Vol 27 (9) ◽  
pp. 095014 ◽  
Author(s):  
Sigbjørn Hervik ◽  
Alan Coley
Keyword(s):  
Scalar Curvature ◽  
Curvature Invariants

scholarly journals KILLING VECTORS IN HIGHER-DIMENSIONAL SPACETIMES WITH CONSTANT SCALAR CURVATURE INVARIANTS

2010 ◽  
Vol 07 (08) ◽  
pp. 1349-1369 ◽  
Author(s):  
DAVID MCNUTT ◽  
NICOS PELAVAS ◽  
ALAN COLEY
Keyword(s):  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Null Vector ◽  
Killing Vectors ◽  
Curvature Invariants ◽  
Higher Dimensional ◽  
Metric Functions ◽  
Kundt Spacetimes

We study the existence of a non-spacelike isometry, ζ, in higher-dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N-dimensional CSI Kundt spacetimes, admitting a non-spacelike isometry, we determine which of these can admit a covariantly constant null vector that also satisfy ζ[a;b] = 0.

scholarly journals On scalar curvature invariants in three dimensional spacetimes

2016 ◽  
Vol 48 (3) ◽  
Author(s):  
N. K. Musoke ◽  
D. D. McNutt ◽  
A. A. Coley ◽  
D. A. Brooks
Keyword(s):  
Scalar Curvature ◽  
Three Dimensional ◽  
Curvature Invariants

scholarly journals Lorentzian manifolds and scalar curvature invariants

2010 ◽  
Vol 27 (10) ◽  
pp. 102001 ◽  
Author(s):  
Alan Coley ◽  
Sigbjørn Hervik ◽  
Nicos Pelavas
Keyword(s):  
Scalar Curvature ◽  
Lorentzian Manifolds ◽  
Curvature Invariants

scholarly journals Universality and Constant Scalar Curvature Invariants

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
A. A. Coley ◽  
S. Hervik
Keyword(s):  
Quantum Theory ◽  
Scalar Curvature ◽  
Classical Solution ◽  
Quantum Correction ◽  
Constant Scalar Curvature ◽  
Curvature Invariants ◽  
Universal Solutions

A classical solution is called universal if the quantum correction is a multiple of the metric. Therefore, universal solutions play an important role in the quantum theory. We show that in a spacetime which is universal all scalar curvature invariants are constant (i.e., the spacetime is CSI).

scholarly journals SPACETIMES WITH ALL SCALAR CURVATURE INVARIANTS IN TERMS OF A COSMOLOGICAL CONSTANT

2013 ◽  
Vol 22 (02) ◽  
pp. 1350003 ◽  
Author(s):  
DAVID McNUTT
Keyword(s):  
Cosmological Constant ◽  
Scalar Curvature ◽  
Riemann Tensor ◽  
Zeroth Order ◽  
Curvature Invariants ◽  
Covariant Derivatives ◽  
Invariant Description ◽  
Scalar Invariants ◽  
Invariant Characterization

In this paper we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth-order curvature invariants expressed as polynomials in Λ, the cosmological constant. Using this invariant description we provide an explicit forms for the metric.

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