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

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.

Lower semicontinuity of mass under C0{C^{0}} convergence and Huisken’s isoperimetric mass

2019 ◽  
Vol 2019 (756) ◽  
pp. 227-257 ◽  
Author(s):  
Jeffrey L. Jauregui ◽  
Dan A. Lee
Keyword(s):  
Scalar Curvature ◽  
Lower Semicontinuity ◽  
Mean Curvature ◽  
Total Mass ◽  
Mean Curvature Flow ◽  
Lower Semicontinuous ◽  
Curvature Flow ◽  
Three Dimensions ◽  
Asymptotically Flat ◽  
Limit Space

AbstractGiven a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed {C^{0}} Cheeger–Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. In other words, total mass is lower semicontinuous under such convergence. In order to prove this, we use Huisken’s isoperimetric mass concept, together with a modified weak mean curvature flow argument. We include a brief discussion of Huisken’s work before explaining our extension of that work. The results are all specific to three dimensions.

scholarly journals Lorentzian spacetimes with constant curvature invariants in three dimensions

2007 ◽  
Vol 25 (2) ◽  
pp. 025008 ◽  
Author(s):  
Alan Coley ◽  
Sigbjørn Hervik ◽  
Nicos Pelavas
Keyword(s):  
Constant Curvature ◽  
Three Dimensions ◽  
Curvature Invariants

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

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 Geometric curve flows in low dimensional Cayley–Klein geometries

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Joseph Benson ◽  
Francis Valiquette
Keyword(s):  
Evolution Equations ◽  
Three Dimensions ◽  
Geometric Flows ◽  
Moving Frames ◽  
Arc Length ◽  
Recursion Operators ◽  
Curvature Invariants ◽  
Curve Flows ◽  
Low Dimensional ◽  
Equivariant Moving Frames

Abstract Using the method of equivariant moving frames, we derive the evolution equations for the curvature invariants of arc-length parametrized curves under arc-length preserving geometric flows in two-, three- and four-dimensional Cayley–Klein geometries. In two and three dimensions, we obtain recursion operators, which show that the curvature evolution equations obtained are completely integrable.

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
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