514 research outputs found
Geometric realizations of generalized algebraic curvature operators
We study the 8 natural GL equivariant geometric realization questions for the
space of generalized algebraic curvature tensors. All but one of them is
solvable; a non-zero projectively flat Ricci antisymmetric generalized
algebraic curvature is not geometrically realizable by a projectively flat
Ricci antisymmetric torsion free connection
Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series
Let G be a compact Lie group acting transitively on Riemannian manifolds M
and N. Let p be a G equivariant Riemannian submersion from M to N. We show that
a smooth differential form on N has finite Fourier series if and only if the
pull back has finite Fourier series on
Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary
We use invariance theory to determine the coefficient
in the supertrace for the twisted de Rham complex with absolute boundary
conditions.Comment: 19 pages, LaTeX, Theorem 1.2 correcte
Design and wind tunnel tests of winglets on a DC-10 wing
Results are presented of a wind tunnel test utilizing a 4.7 percent scale semi-span model in the Langley Research Center 8-foot transonic pressure wind tunnel to establish the cruise drag improvement potential of winglets as applied to the DC-10 wide body transport aircraft. Winglets were investigated on both the DC-10 Series 10 (domestic) and 30/40 (intercontinental) configurations and compared with the Series 30/40 configuration. The results of the investigation confirm that for the DC-10 winglets provide approximately twice the cruise drag reduction of wing-tip extensions for about the same increase in bending moment at the wing fuselage juncture. Furthermore, the winglet configurations achieved drag improvements which were in close agreement to analytical estimates. It was observed that relatively small changes in wing-winglet tailoring effected large improvements in drag and visual flow characteristics. All final winglet configurations exhibited visual flow characteristics on the wing and winglet
Euclidean Scalar Green Function in a Higher Dimensional Global Spacetime
We construct the explicit Euclidean scalar Green function associated with a
massless field in a higher dimensional global monopole spacetime, i.e., a
-spacetime with which presents a solid angle deficit. Our
result is expressed in terms of a infinite sum of products of Legendre
functions with Gegenbauer polynomials. Although this Green function cannot be
expressed in a closed form, for the specific case where the solid angle deficit
is very small, it is possible to develop the sum and obtain the Green function
in a more workable expression. Having this expression it is possible to
calculate the vacuum expectation value of some relevant operators. As an
application of this formalism, we calculate the renormalized vacuum expectation
value of the square of the scalar field, , and the
energy-momentum tensor, , for the global monopole
spacetime with spatial dimensions and .Comment: 18 pages, LaTex format, no figure
Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms
The Hodge--de Rham Laplacian on spheres acting on antisymmetric tensor fields
is considered. Explicit expressions for the spectrum are derived in a quite
direct way, confirming previous results. Associated functional determinants and
the heat kernel expansion are evaluated. Using this method, new non--local
counterterms in the quantum effective action are obtained, which can be
expressed in terms of Betti numbers.Comment: LaTeX, 22 pages, no figure
On the geometric boundaries of hyperbolic 4-manifolds
We provide, for hyperbolic and flat 3-manifolds, obstructions to bounding
hyperbolic 4-manifolds, thus resolving in the negative a question of Farrell
and Zdravkovska.Comment: 8 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper5.abs.htm
Nilpotent noncommutativity and renormalization
We analyze renormalizability properties of noncommutative (NC) theories with
a bifermionic NC parameter. We introduce a new 4-dimensional scalar field model
which is renormalizable at all orders of the loop expansion. We show that this
model has an infrared stable fixed point (at the one-loop level). We check that
the NC QED (which is one-loop renormalizable with usual NC parameter) remains
renormalizable when the NC parameter is bifermionic, at least to the extent of
one-loop diagrams with external photon legs. Our general conclusion is that
bifermionic noncommutativity improves renormalizablility properties of NC
theories.Comment: 5 figures, a reference adde
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