1,071 research outputs found
On Non Commutative G2 structure
Using an algebraic orbifold method, we present non-commutative aspects of
structure of seven dimensional real manifolds. We first develop and solve
the non commutativity parameter constraint equations defining manifold
algebras. We show that there are eight possible solutions for this extended
structure, one of which corresponds to the commutative case. Then we obtain a
matrix representation solving such algebras using combinatorial arguments. An
application to matrix model of M-theory is discussed.Comment: 16 pages, Latex. Typos corrected, minor changes. Version to appear in
J. Phys.A: Math.Gen.(2005
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
M-theory Compactifications on Manifolds with G2 Structure
In this paper we study M-theory compactifications on manifolds of G2
structure. By computing the gravitino mass term in four dimensions we derive
the general form for the superpotential which appears in such compactifications
and show that beside the normal flux term there is a term which appears only
for non-minimal G2 structure. We further apply these results to
compactifications on manifolds with weak G2 holonomy and make a couple of
statements regarding the deformation space of such manifolds. Finally we show
that the superpotential derived from fermionic terms leads to the potential
that can be derived from the explicit compactification, thus strengthening the
conjectures we make about the space of deformations of manifolds with weak G2
holonomy.Comment: 34 pages. Minor changes: typos corrected, references added. Version
to appear in Class. Quantum Gra
Sasakian Geometry, Holonomy, and Supersymmetry
In this expository article we discuss the relations between Sasakian
geometry, reduced holonomy and supersymmetry. It is well known that the
Riemannian manifolds other than the round spheres that admit real Killing
spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly
parallel G2 structure, and nearly Kaehler 6-manifolds. We then discuss the
relations between the latter two and Sasaki-Einstein geometry.Comment: 40 pages, some minor corrections made, to appear in the Handbook of
pseudo-Riemannian Geometry and Supersymmetr
G2-structures for N=1 supersymmetric AdS4 solutions of M-theory
We study the N=1 supersymmetric solutions of D=11 supergravity obtained as a
warped product of four-dimensional anti-de-Sitter space with a
seven-dimensional Riemannian manifold M. Using the octonion bundle structure on
M we reformulate the Killing spinor equations in terms of sections of the
octonion bundle on M. The solutions then define a single complexified
G2-structure on M or equivalently two real G2-structures. We then study the
torsion of these G2-structures and the relationships between them.Comment: 48 pages, updated references, corrected minor errors and typos,
Class. Quantum Grav. (2018
- …