The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n − 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be th...

Abstract Let ( X , J ) be a nilmanifold with an invariant nilpotent complex structure. We study the existence of p -Kähler structures (which include Kähler and balanced metrics) on . More precisely, we determine optimal such that there are no Finally, show that, contrarily to case, compact manifolds is relation between metrics degeneracy step Frölicher spectral sequence. can arbitrarily large.

The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space T of oriented affine lines in R with the tangent bundle of S. Thus, the round metric on S induces a Kähler structure on T which turns out to have a metric of neutral signature. It is shown that the isometry group of this metric is isomorphic to the isometry g...

In this note, using Calabi’s method, we construct rotationally symmetric KählerRicci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification, where the curvature of hermitian line bundle is Kähler-Einstein. These examples generalize the construction of Koiso, Cao and Feldman-Ilmanen-Knopf. 1 A little motivation In [1], the authors constructed...

We show that the natural S-bundle over a projective special Kähler manifold carries the geometry of a proper affine hypersphere endowed with a Sasakian structure. The construction generalizes the geometry of the Hopf-fibration S −→ CPn in the context of projective special Kähler manifolds. As an application we have that a natural circle bundle over the Kuranishi moduli space of a Calabi-Yau thr...

1 The dynamics of quasicrystals, the dynamics of Kähler action, symbolic dynamics, and the dynamics of self-organization 1 1.1 The non-determinism for the dynamics of quasicrystals contra non-determinism of Kähler action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The dynamics of quasicrystals as a model for fundamental dynamics or high level symbolic...

Kähler quantization of H(T,R) is studied. It is shown that this theory corresponds to a fermionic σ-model targeting a noncommutative space. By solving the complex-structure moduli independence conditions, the quantum background independent wave function is obtained. We study the transformation of the wave function under modular transformation. It is shown that the transformation rule is charact...

Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-1 holomorphic sub-bundle D ⊂ TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler manifold (M, g). If Z also admits a second complex contact structure D̃ 6= D, then Z = C...