3,739 research outputs found
Global symplectic coordinates on gradient Kaehler-Ricci solitons
A classical result of D. McDuff asserts that a simply-connected complete
Kaehler manifold with non positive sectional curvature admits
global symplectic coordinates through a symplectomorphism (where is the complex dimension of ), satisfying the following
property (proved by E. Ciriza): the image of any complex totally
geodesic submanifold through the point such that ,
is a complex linear subspace of . The aim of this paper is
to exhibit, for all positive integers , examples of -dimensional complete
Kaehler manifolds with non-negative sectional curvature globally
symplectomorphic to through a symplectomorphism satisfying Ciriza's
property.Comment: 8 page
Finite TYCZ expansions and cscK metrics
Let be a Kaehler manifold whose associated Kaehler form is
integral and let be a quantization hermitian
line bundle. In this paper we study those Kaehler manifolds admitting
a finite TYCZ expansion. We show that if the TYCZ expansion is finite then
is indeed a polynomial in of degree , , and the
log-term of the Szeg\"{o} kernel of the disc bundle vanishes
(where is the dual bundle of ). Moreover, we provide a complete
classification of the Kaehler manifolds admitting finite TYCZ expansion either
when is a complex curve or when is a complex surface with a cscK metric
which admits a radial Kaehler potential
Balanced metrics on Cartan and Cartan-Hartogs domains
This paper consists of two results dealing with balanced metrics (in S.
Donaldson terminology) on nonconpact complex manifolds. In the first one we
describe all balanced metrics on Cartan domains. In the second one we show that
the only Cartan-Hartogs domain which admits a balanced metric is the complex
hyperbolic space. By combining these results with those obtained in [13]
(Kaehler-Einstein submanifolds of the infinite dimensional projective space, to
appear in Mathematische Annalen) we also provide the first example of complete,
Kaehler-Einstein and projectively induced metric g such that is not
balanced for all .Comment: 11 page
An algorithm for the quadratic approximation
The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression
for the polynomial coefficients of the quadratic approximation is
given. A recursive algorithm for the construction of these coefficients
is derived. The algorithm constructs a table of quadratic
approximations analogous to the Pade table of rational approximations
An algorithm for the quadratic approximation
The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression
for the polynomial coefficients of the quadratic approximation is
given. A recursive algorithm for the construction of these coefficients
is derived. The algorithm constructs a table of quadratic
approximations analogous to the Pade table of rational approximations
Balanced metrics on homogeneous vector bundles
Let be a holomorphic vector bundle over a compact Kaehler
manifold and let be its
decomposition into irreducible factors. Suppose that each admits a
-balanced metric in Donaldson-Wang terminology. In this paper we prove
that admits a unique -balanced metric if and only if
for all , where denotes
the rank of and . We apply our result to the case
of homogeneous vector bundles over a rational homogeneous variety
and we show the existence and rigidity of balanced Kaehler embedding from into Grassmannians.Comment: 5 page
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