2.
Brackets, forms and invariant functionals - Hitchin, Nigel
In the context of generalized geometry we first show how the Courant bracket helps to define connections with skew torsion and then investigate a five-dimensional invariant functional and its associated geometry, which involves three Courant-commuting sections of $T \bigoplus T\sp *$ . A Hamiltonian flow arising from this corresponds to a version of the Nahm equations, and we investigate the sixdimensional geometrical structure this describes.
3.
On the geometry of almost complex 6-manifolds - Bryant, Robert L.
This article discusses some basic geometry of almost complex 6-manifolds. A 2-parameter family of intrinsic first-order functionals on almost complex structures on 6-manifolds is introduced and their Euler-Lagrange equations are computed.
¶ A natural generalization of holomorphic bundles over complex manifolds to the almost complex case is introduced. The general almost complex manifold will not admit any nontrivial bundles of this type, but there is a class of nonintegrable almost complex manifolds for which there are such
nontrivial bundles. For example, the $G_2$-invariant almost complex structure on the 6-sphere admits such nontrivial bundles. This class of almost complex manifolds in dimension 6...
10.
The Baouendi-Treves approximation theorem for continuous vector fields - Berhanu, Shiferaw; Hounie, Jorge
This article establishes the Baouendi-Treves approximation theorem for locally integrable structures whose vector fields have continuous coefficients. As a consequence, some uniqueness results are derived.
13.
$rec.titulo - Eastwood, Michael
The twistor construction in Euclidean 4-space may be based on the algebra of quaternions. A counterpart to this construction is established in split signature by using the split
quaternions.
19.
The Boundary Behavior of Holomorphic Functions: Global and Local Results - Krantz, Steven G.
We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $\Omega$ -- both in one and several complex variables. The approach involves two new localized maximal functions.
¶ As a result of this methodology, theorems of Calderón type about local boundary behavior on a set of positive measure may be proved in a new and more natural way.
¶ We also study the question of nontangential boundedness (on a set of positive measure) versus admissible boundedness. Under suitable hypotheses, these two conditions are shown to be equivalent.
1.
