Related papers: Hyperk\"ahler manifolds

We use Heegaard splittings to give some examples of virtually Haken 3-manifolds.

In this note, we make two methodical observations. $\bullet$ We prove in a simple explicit way that a necessary and sufficient condition for a K\"ahler manifold to be hyperk\"ahler is $h_{i\bar k} h_{j\bar l } \Omega^{\bar k \bar l} \ =\ C…

This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…

We provide a natural interpretation of the secondary Euler characteristic and introduce higher Euler characteristics. For a compact oriented manifold of odd dimension, the secondary Euler characteristic recovers the Kervaire…

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic…

We survey the properties of Brody and Kobayashi hyperbolic manifolds.

Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperk\"ahlerian manifolds as stated by Verbitsky. The initial purpose of this document (which was prepared for a seminar talk) was to extract the…

We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperk\"ahler manifolds. Using an action of these groups on some non-positively curved space, we deduce many of their properties, including finite presentation,…

We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…

We review old and new properties of Hopf manifolds from the point of view of their analytic and metric structure.

We revisit Allendoerfer-Weil's formula for the Euler characteristic of embedded hypersurfaces in constant sectional curvature manifolds, first taking some time to re-prove it while demonstrating techniques of [2] and then applying it to…

We discuss symplectic and hyperk\"ahler implosion and present candidates for the symplectic duals of the universal hyperk\"ahler implosion for various groups.

A hyperk\"ahler manifold is defined as a Riemannian manifold endowed with three covariantly constant complex structures that are quaternionically related. A twistor space is characterized as a holomorphic fiber bundle $p: \mathcal{Z}…

We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.

We study the intersection form $F_X$ on the second cohomology group $H^2(X, \mathbb{Z})$ of a compact K\"ahler manifold $X$ of dimension $n$. Although the structure of $F_X$ is relatively well understood in dimensions two and three, much…

A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.

In this paper we showed that every connected extremal K\"ahler submanifold of a complex projetive space has a natural extension which is a complete K\"ahler manifold and admits a holomorphic isometric immersion into the same ambient space.…

In this paper, we introduce the notion of F-manifold color algebras and study their properties which extend some results for F-manifold algebras.

We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main…

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.