4,594 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
Kahler manifolds and their relatives
Let M1 and M2 be two K¨ahler manifolds. We call M1 and M2 relatives if they share a non-trivial K¨ahler submanifold S, namely, if there exist two holomorphic and isometric immersions (K¨ahler immersions) h1 : S → M1 and h2 : S → M2. Moreover, two K¨ahler manifolds M1 and M2 are said to be weakly relatives if there exist two locally isometric (not necessarily holomorphic) K¨ahler manifolds S1 and S2 which admit two K¨ahler immersions into M1 and M2 respectively. The notions introduced are not equivalent (cf. Example 2.3). Our main results in this paper are Theorem 1.2 and Theorem 1.4. In the first theorem we show that a complex bounded domain D ⊂ Cn with its Bergman metric and a projective K¨ahler manifold (i.e. a projective manifold endowed with the restriction of the Fubini-Study metric) are not relatives. In the second theorem we prove that a Hermitian symmetric space of noncompact type and a projective K¨ahler manifold are not weakly relatives. Notice that the proof of the second result does not follows trivially from the first one. We also remark that the above results are of local nature, i.e. no assumptions are used about the compactness or completeness of the manifolds involve
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
Symplectic duality between complex domains
In this paper after extending the denition of symplectic duality (given in [3] for bounded symmetric domains ) to arbitrary complex domains of Cn centered at the origin we generalize some of the results proved in [3] and [4] to those domain
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
Embeddings of metric Boolean algebras in RN
A Boolean algebra A equipped with a (finitely-additive) positive probability measure m can be turned into a metric space (A,dm), where dm(a,b)=m((a∧¬b)∨(¬a∧b)), for any a,b∈A, sometimes referred to as metric Boolean algebra. In this paper, we study under which conditions the space of atoms of a finite metric Boolean algebra can be isometrically embedded in RN (for a certain N) equipped with the Euclidean metric. In particular, we characterize the topology of the positive measures over a finite algebra A such that the metric space (At(A),dm) embeds isometrically in RN (with the Euclidean metric
Probability over Płonka sums of Boolean algebras: States, metrics and topology
The paper introduces the notion of state for involutive bisemilattices, a variety which plays the role of algebraic counterpart of weak Kleene logics and whose elements are represented as Płonka sums of Boolean algebras. We investigate the relations between states over an involutive bisemilattice and probability measures over the (Boolean) algebras in the Płonka sum representation and, the direct limit of these algebras. Moreover, we study the metric completion of involutive bisemilattices, as pseudometric spaces, and the topology induced by the pseudometric
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
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