724 research outputs found
On invariants of almost symplectic connections
We study the irreducible decomposition under Sp(2n, R) of the space of
torsion tensors of almost symplectic connections. Then a description of all
symplectic quadratic invariants of torsion-like tensors is given. When applied
to a manifold M with an almost symplectic structure, these instruments give
preliminary insight for finding a preferred linear almost symplectic connection
on M . We rediscover Ph. Tondeur's Theorem on almost symplectic connections.
Properties of torsion of the vectorial kind are deduced
Development of explosive forming techniques for Saturn V components Final report, 24 Jun. 1964 - 28 Jan. 1966
Explosive forming techniques development for aluminum alloy, carbon steel, and titanium components for Saturn V launch vehicl
The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard Model
The correlation of the fractionally represented hypercharge group with the
isospin and colour group in the standard model determines as faithfully
represented internal group the quotient group
{\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}. The discrete cyclic central
abelian-nonabelian internal correlation involved is considered with respect to
its consequences for the representations by the standard model fields, the
electroweak mixing angle and the symmetry breakdown. There exists a further
discrete -correlation between chirality and Lorentz properties and also a
continuous \U(1)-external-internal one between hyperisospin and chirality.Comment: 18 pages, latex, macros include
Killing spinors in supergravity with 4-fluxes
We study the spinorial Killing equation of supergravity involving a torsion
3-form \T as well as a flux 4-form \F. In dimension seven, we construct
explicit families of compact solutions out of 3-Sasakian geometries, nearly
parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The
constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We
investigate the constraint \T \cdot \Psi = 0, too, and show that it singles
out a very special choice of numerical parameters in the Killing equation,
which can also be justified geometrically
Composition algebras and the two faces of
We consider composition and division algebras over the real numbers: We note
two r\^oles for the group : as automorphism group of the octonions and
as the isotropy group of a generic 3-form in 7 dimensions. We show why they are
equivalent, by means of a regular metric. We express in some diagrams the
relation between some pertinent groups, most of them related to the octonions.
Some applications to physics are also discussed.Comment: 11 pages, 3 figure
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
The G_2 sphere over a 4-manifold
We present a construction of a canonical G_2 structure on the unit sphere
tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such
structure is never geometric or 1-flat, but seems full of other possibilities.
We start by the study of the most basic properties of our construction. The
structure is co-calibrated if, and only if, M is an Einstein manifold. The
fibres are always associative. In fact, the associated 3-form results from a
linear combination of three other volume 3-forms, one of which is the volume of
the fibres. We also give new examples of co-calibrated structures on well known
spaces. We hope this contributes both to the knowledge of special geometries
and to the study of 4-manifolds.Comment: 13 page
Explosive forming of 2219 aluminum final report
Variables affecting metal springback of aluminum during explosive deformation and influence of high energy forming on metallurgical behavio
Generalised -manifolds
We define new Riemannian structures on 7-manifolds by a differential form of
mixed degree which is the critical point of a (possibly constrained)
variational problem over a fixed cohomology class. The unconstrained critical
points generalise the notion of a manifold of holonomy , while the
constrained ones give rise to a new geometry without a classical counterpart.
We characterise these structures by the means of spinors and show the
integrability conditions to be equivalent to the supersymmetry equations on
spinors in supergravity theory of type IIA/B with bosonic background fields. In
particular, this geometry can be described by two linear metric connections
with skew torsion. Finally, we construct explicit examples by using the device
of T-duality.Comment: 27 pages. v2: references added. v3: wrong argument (Theorem 3.3) and
example (Section 4.1) removed, further examples added, notation simplified,
all comments appreciated. v4:computation of Ricci tensor corrected, various
minor changes, final version of the paper to appear in Comm. Math. Phy
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