Related papers: An Indefinite Kaehler Metric on the Space of Orien…

We study the neutral K\"ahler metric on the space of time-like lines in Lorentzian ${\Bbb{E}}^3_1$, which we identify with the total space of the tangent bundle to the hyperbolic plane. We find all of the infinitesimal isometries of this…

We find a family of K\"ahler metrics invariantly defined on the radius $r_0>0$ tangent disk bundle ${{\cal T}_{M,r_0}}$ of any given real space-form $M$ or any of its quotients by discrete groups of isometries. Such metrics are complete in…

We study the totally null surfaces of the neutral Kaehler metric on certain 4-manifolds. The tangent spaces of totally null surfaces are either self-dual ($\alpha$-planes) or anti-self-dual ($\beta$-planes) and so we consider…

Obstruction flatness of a strongly pseudoconvex hypersurface $\Sigma$ in a complex manifold refers to the property that any (local) K\"ahler-Einstein metric on the pseudoconvex side of $\Sigma$, complete up to $\Sigma$, has a potential…

In this paper we study the geometry of the total space $Y$ of a cotangent bundle to a K\"ahler manifold $N$ where $N$ is obtained as a K\"ahler reduction from $\mathbb C^n$. Using the hyperk\"ahler reduction we construct a hyperk\"ahler…

We prove that the space of convex real projective structures on a surface of genus $g\ge 2$ admits a mapping class group invariant K\"ahler metric where Teichm\"uller space with Weil-Petersson metric is a totally geodesic complex…

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…

We study 2-dimensional submanifolds of the space ${\mathbb{L}}({\mathbb{H}}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral K\"ahler structure. Such a surface is Lagrangian iff there exists a surface in…

We construct metrics with the holonomy group SU(2) on the tangent bundles of weighted complex projective lines and give a geometric description of the moduli space of special Kahler metrics on a K3-surface in the neighborhood of the flat…

Given an oriented Riemannian surface $(\Sigma, g)$, its tangent bundle $T\Sigma$ enjoys a natural pseudo-K\"{a}hler structure, that is the combination of a complex structure $\J$, a pseudo-metric $\G$ with neutral signature and a symplectic…

In this paper the classification of left-invariant Riemannian metrics, up to the action of the automorphism group, on cotangent bundle of (2n+1)-dimensional Heisenberg group is presented. Also, it is proved that the complex structure on…

We classify K\"ahler-Einstein manifolds which admit a K\"ahler immersion into a finite dimensional complex projective space endowed with the Fubini-Study metric, whose codimention is not greater than 3 and whose metric is rotation…

In this paper we propose and investigate in full generality new notions of (continuous, non-isometric) symmetry on hyperk\"ahler spaces. These can be grouped into two categories, corresponding to the two basic types of continuous…

Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with fixed boundary conditions. Then the infinite-dimensional manifold S carries a natural…

A canonical hyperkaehler metric on the total space $T^*M$ of a cotangent bundle to a complex manifold $M$ has been constructed recently by the author (see alg-geom/9710026). This paper presents the results of alg-geom/9710026 in a…

A Hermitian metric $\omega$ on a complex manifold is called SKT or pluriclosed if $dd^c\omega=0$. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case…

In this article, we construct a new para-K\"ahler structure $({\mathcal G},{\mathcal J},\Omega)$ in the space of oriented geodesics ${\mathbb L}(M)$ in a non-flat, real space form $M$. We first show that the para-K\"ahler metric ${\mathcal…

For a connected Lie group G, we show that a complex structure on the total space TG of the tangent bundle of G that is left invariant and has the property that each left translation G-orbit is a totally real submanifold is induced from a…

We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism of the tangent bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in the…

Motivated by the picture of mirror symmetry suggested by Strominger, Yau and Zaslow, we made a conjecture concerning the Gromov-Hausdorff limits of Calabi-Yau n-folds (with Ricci-flat K\"ahler metric) as one approaches a large complex…