For a fixed prequantum line bundle L over a hyperKähler manifold X, we find a natural Sp (1)-
action on Ω∗(X, L) intertwining a twistor family of Spin c-Dirac Laplacians on the spaces of L …

Specifying an almost quaternionic structure Q on a 4n-manifold M is equivalent to specifying
a twistor bundle Z (Q)−→ M. When Q is invariant under a torsion free connection, Z (Q) can …

The generalized hypercomplex structures defined within the framework of generalized
geometry include hypercomplex and holomorphic symplectic structures as particular cases …

This submission is a PhD dissertation. Kapustin and Witten conjectured that there is a mirror
symmetry relation between the hyperk\" ahler structures on certain Higgs bundle moduli …

We study the moduli space M of twisted Hermite-Einstein connections on a vector bundle
over a K3 surface X. We show that the universal bundle can be viewed as a family of stable …

Munir une variété M de dimension 4 n d'une structure presque quaternionique Q revient
précisément à lui associer un fibré des twisteurs Z (Q)⟶ M. Lorsque Q est stable par une …

Rozansky and Witten [31] described a sigma model based on maps from a three-
dimensional manifold to a hyperkähler manifold, yielding invariants of both. A perturbative …

The twistor construction for Riemannian manifolds is extended to the case of manifolds
endowed with generalized metrics (in the sense of generalized geometry à la Hitchin). The …

In this research we utilized complex structure in ܴଷ to construct geometrical solutions for
Laplace equation, wave equation and monopole equation. The complex space used is the …

To give an almost quaternionic structure on a 4n-manifold $ M $ is equivalent to give its
bundle of twistors $ Z (Q)\longrightarrow M $. When $ Q $ is invariant under a torsion free …