152 research outputs found
Octonionic Gravitational Instantons
We construct eight-dimensional gravitational instantons by solving
appropriate self-duality equations for the spin-connection. The particular
gravitational instanton we present has holonomy and, in a sense, it
is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a
removable bolt singularity which is topologically S^4 and its boundary at
infinity is the squashed S^7. We also lift our solutions to ten and eleven
dimensions and construct fundamental string and membrane configurations that
preserve 1/16 of the original supersymmetries.Comment: 17 pages, latex, no figures. References to earlier works adde
Eight-Dimensional Self-Dual Spaces
We discuss higher-dimensional gravitational instantons by studying
appropriate self-duality equations for the spin connection. In seven and in
eight dimensions, the corresponding spaces admit a covariantly constant spinor
and have holonomies in G_2 and Spin(7), respectively. We find a non-compact
solution to the self-duality equations in eight dimensions in which the
self-dual space has an elliptically-fibered structure.Comment: 16 pages, late
The effects of room design on computer-supported collaborative learning in a multi-touch classroom.
While research indicates that technology can be useful for supporting learning and collaboration, there is still relatively little uptake or widespread implementation of these technologies in classrooms. In this paper, we explore one aspect of the development of a multi-touch classroom, looking at two different designs of the classroom environment to explore how classroom layout may influence group interaction and learning. Three classes of students working in groups of four were taught in the traditional forward-facing room condition, while three classes worked in a centered room condition. Our results indicate that while the outcomes on tasks were similar across conditions, groups engaged in more talk (but not more off-task talk) in a centered room layout, than in a traditional forward-facing room. These results suggest that the use of technology in the classroom may be influenced by the location of the technology, both in terms of the learning outcomes and the interaction behaviors of students. The findings highlight the importance of considering the learning environment when designing technology to support learning, and ensuring that integration of technology into formal learning environments is done with attention to how the technology may disrupt, or contribute to, the classroom interaction practices
On the geometry of closed G2-structure
We give an answer to a question posed recently by R.Bryant, namely we show
that a compact 7-dimensional manifold equipped with a G2-structure with closed
fundamental form is Einstein if and only if the Riemannian holonomy of the
induced metric is contained in G2. This could be considered to be a G2 analogue
of the Goldberg conjecture in almost Kahler geometry. The result was
generalized by R.L.Bryant to closed G2-structures with too tightly pinched
Ricci tensor. We extend it in another direction proving that a compact
G2-manifold with closed fundamental form and divergence-free Weyl tensor is a
G2-manifold with parallel fundamental form. We introduce a second symmetric
Ricci-type tensor and show that Einstein conditions applied to the two Ricci
tensors on a closed G2-structure again imply that the induced metric has
holonomy group contained in G2.Comment: 14 pages, the Einstein condition in the assumptions of the Main
theorem is generalized to the assumption that the Weyl tensor is
divergence-free, clarity improved, typos correcte
Axisymmetric non-abelian BPS monopoles from G_2 metrics
Exact self-gravitating BPS global monopoles in four
dimensions are constructed by dimensional reduction of eight dimensional
metrics with holonomy asymptotic to cones over . The
solutions carry two topological charges in an interesting way. They are
generically axially but not spherically symmetric. This last fact is related to
the isometries and asymptotic topology of the metrics. It is further
shown that some metrics known numerically reduce to supersymmetric cosmic
strings.Comment: Latex. 1+21 pages. References update
Dirac equation on a G_2 manifold
We find a large family of solutions to the Dirac equation on a manifold of
holonomy asymptotic to a cone over , including all radial
solutions. The behaviour of these solutions is studied as the manifold
developes a conical singularity. None of the solutions found are both localised
and square integrable at the origin. This result is consistent with the absence
of chiral fermions in M-theory on the conifold over . The
approach here is complementary to previous analyses using dualities and anomaly
cancellation.Comment: 1+11 pages. LaTeX. Minor rewording in introduction and conclusio
Type IIA Orientifold Limit of M-Theory on Compact Joyce 8-Manifold of Spin(7)-Holonomy
We show that M-theory compactified on a compact Joyce 8-manifold of
-holonomy, which yields an effective theory in with = 1
supersymmetry, admits at some special points in it moduli space a description
in terms of type IIA theory on an orientifold of compact Joyce 7-manifold of
-holonomy. We find the evidence in favour of this duality by computing the
massless spectra on both M-thory side and type IIA side. For the latter, we
compute the massless spectra by going to the orbifold limit of the Joyce
7-manifold.Comment: 26 pages, 2 eps figures, Latex file, two references and one footnote
added, corrected some typo
Holonomy of Einstein Lorentzian manifolds
The classification of all possible holonomy algebras of Einstein and vacuum
Einstein Lorentzian manifolds is obtained. It is shown that each such algebra
appears as the holonomy algebra of an Einstein (resp., vacuum Einstein)
Lorentzian manifold, the direct constructions are given. Also the holonomy
algebras of totally Ricci-isotropic Lorentzian manifolds are classified. The
classification of the holonomy algebras of Lorentzian manifolds is reviewed and
a complete description of the spaces of curvature tensors for these holonomies
is given.Comment: Dedicated to to Mark Volfovich Losik on his 75th birthday. This
version is an extended part of the previous version; another part of the
previous version is extended and submitted as arXiv:1001.444
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