Related papers: Geometric realizations of affine Kaehler curvature…

In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.

For every fibration $f : X \to B$ with $X$ a compact K\"ahler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.

We prove that every compact K\"ahler threefold has arbitrarily small deformations to some projective manifolds, thereby solving the Kodaira problem in dimension 3.

We prove that every projective special K\"ahler manifold with \emph{regular boundary behaviour} is complete and defines a family of complete quaternionic K\"ahler manifolds depending on a parameter $c\ge 0$. We also show that, irrespective…

We prove that a Kahler manifold with positive bisectional curvature and maximal diameter is isometric to the complex projective space with the Fubini-Study metric.

This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…

We study the Kaehler metric given by the logarithm of a cubic form on its complexified index cone. Under mirror symmetry, this metric should asymptotically correspond to the Weil-Petersson metric. Using the theory of special Kaehler…

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with…

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…

Two Kaehler metrics on one complex manifold are said to be c-projectively equivalent if their J-planar curves, i.e., curves defined by the property that their acceleration is complex proportional to their velocity, coincide. The degree of…

We survey some recent results and constructions of almost-K\"ahler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.

An affine manifold is said to be geodesically complete if all affine geodesics extend for all time. It is said to be affine Killing complete if the integral curves for any affine Killing vector field extend for all time. We use the solution…

We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.

We prove that any Kaehler manifold admitting a flat complex conformal connection is a Bochner-Kaehler manifold with special scalar distribution and zero geometric constants. Applying the local structural theorem for such manifolds we obtain…

We study the basic geometric properties of an indefinite locally conformal Kaehler manifold.

In this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras.

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the K\"ahler geometry of a finite dimensional complex projective spaces.

We prove compactification theorems for some complete K\"ahler manifolds with nonnegative Ricci curvature. Among other things, we prove that a complete noncompact K\"ahler Ricci flat manifold with maximal volume growth and quadratic…

In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.