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Andrea Spiro

Publications and source records attributed to Andrea Spiro.

48 records · Page 3Linked to original sources
arXiv2008

On the localization principle for the automorphisms of pseudoellipsoids

We show that Alexander's extendibility theorem for a local automorphism of the unit ball is valid also for a local automorphism $f$ of a pseudoellipsoid $\E^n_{(p_1, ..., p_{k})} \= \{z \in \C^n : \sum_{j= 1}^{n - k}|z_j|^2 + |z_{n-k+1}|^{2 p_1} + ... + |z_n|^{2 p_{k}} < 1 \}$, provided that $f$ is defined on a region $\U \subset \E^n_{(p)}$ such that: i) $\partial \U \cap \partial \E^n_{(p)}$ contains an open set of strongly pseudoconvex points; ii) $\U \cap \{z_i = 0 \} \neq \emptyset$ for any $n-k +1 \leq i \leq n$. By the counterexamples we exhibit, such hypotheses can be considered as optimal.

math.CV↗
arXiv2007

Monge-Ampere equations and moduli spaces of manifolds of circular type

A (bounded) manifold of circular type is a complex manifold M of dimension n admitting a (bounded) exhaustive real function u, defined on M minus a point x_o, so that: a) it is a smooth solution on $M\setminus {x_o}$ to the Monge-Ampère equation $(d d^c u)^n = 0$; b) x_o is a singular point for u of logarithmic type and e^u extends smoothly on the blow up of M at x_o; c) $d d^c (e^u) >0$ at any point of $M\setminus {x_o}$. This class of manifolds naturally includes all smoothly bounded, strictly linearly convex domains and all smoothly bounded, strongly pseudoconvex circular domains of $\bC^n$. The moduli spaces of bounded manifolds of circular type are studied. In particular, for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form. It is also shown that the class of normalizing maps for an n-dimensional manifold M is a new holomorphic invariant with the following property: it is parameterized by the points of a finite dimensional real manifold of dimension n^2 when M is a (non-convex) circular domain while it is of dimension $n^2 + 2 n$ when M is a strictly convex domain. New characterizations of the circular domains and of the unit ball are also obtained.

math.CV↗
arXiv2006

Kaehler-Ricci solitons on homogeneous toric bundles (I)

This is the first of a sequence of two papers. Here, a simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold G^C/P is provided in terms of symplectic data. The result of this paper is used in the second paper, where it is proved that an homogeneous toric bundle over a flag manifold admits a Kaehler-Ricci solitonic metric if and only if it is Fano.

math.DG↗
arXiv2006

Kaehler-Ricci solitons on homogeneous toric bundles (II)

It is proved that an homogeneous toric bundles over a flag manifold G^\C/P admits a Kaehler-Ricci solitonic metric if and only if it is Fano. In particular, an homogeneous toric bundle of this kind is Kaehler-Einstein if and only if it is Fano and its Futaki invariant vanishes identically.

math.DG↗
arXiv2005

Total reality of conormal bundles of hypersurfaces in almost complex manifolds

A generalization to the almost complex setting of a well-known result by S. Webster is given. Namely, we prove that if $Γ$ is a strongly pseudoconvex hypersurface in an almost complex manifold $(M, J)$, then the conormal bundle of $Γ$ is a totally real submanifold of $(T^*M, \J)$, where $\J$ is the lifted almost complex structure on $T^*M$ defined by Ishihara and Yano.

math.DG↗
arXiv2005

An existence theorem for stationary discs in almost complex manifolds

An existence theorem for stationary discs of strongly pseudoconvex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces there exists a unique stationary disc passing through that point and tangent to the given vector.

math.CV↗
arXiv2004

Explicit construction of a Chern-Moser connection for CR manifolds of codimension two

In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codimension two, i.e. a pair (P, w), consisting of a principal bundle P over M and of a Cartan connection form w on P, satisfying the following property: the (local) CR transformations of M are in one to one correspondence with the (local) automorphisms of P which preserve w. For any point x in M, this construction determines an explicit immersion of the stability subalgebra Lie(aut(M)_x) into the Lie algebra Lie(H) of the structure group H of P.

math.DG↗
arXiv2001

Running after a new Kaehler-Einstein metric

We deal with compact Kaehler manifolds M which are acted on by a semisimple compact Lie group G of isometries with codimension one regular orbits. We provide an explicit description of the standard blow-ups of such manifolds along complex singular orbits, in case b_1(M) = 0 and the regular orbits are Levi nondegenerate. Up to very few exceptions, all the nonhomogeneous manifolds in this class are shown to admit a G-invariant Kaehler-Einstein metric, giving completely new examples of compact Kaehler-Einstein manifolds.

math.DG↗
arXiv2001

The Ricci tensor of an almost homogenous Kaehler manifold

We determine an explicit expression for the Ricci tensor of a K-manifold, that is of a compact Kaehler manifold M with vanishing first Betti number, on which a semisimple group G of biholomorphic isometries acts with an orbit of codimension one. We also prove that the Kaehler form and the Ricci form of M are uniquely determined by two special curves with values in g = Lie(G), say Z, Z': R \to g = Lie(G) and we show how the curve Z' is determined by the curve Z. These results are used in another work with F. Podesta', where new examples of non-homogeneous compact Kaehler-Einstein manifolds with positive first Chern class are constructed.

math.DG↗
arXiv1999

The Structure Equations of a Complex Finsler Manifold

For a strongly pseudo-convex complex Finsler manifold M, a bundle U of adapted unitary frames is canonically defined. A non-linear Hermitian connection on U, invariant under local biholomorphic isometries, is given and it proved to be unique. By means of such connection, an absolute parallelism on U is determined and a new set of structure functions which generate all the isometric invariants of a Finsler metric is obtained. A pseudo-convex complex Finsler manifolds M, which admits a totally geodesic complex curve with a given constant holomorphic sectional curvature through any point and any direction, is called E-manifold. Main examples of E-manifolds are the smoothly bounded, strictly convex domains in C^n, endowed with the Kobayashi metric. A complete characterization of E-manifolds, using the previously defined structure functions, is given and a smaller set of generating functions for the isometric invariants of E-manifolds is determined.

math.DG↗