3,168 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
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
Kahler–Ricci Solitons Induced by Infinite-Dimensional Complex Space Forms
We exhibit families of nontrivial (i.e., not Kähler–Einstein) radial Kähler– Ricci solitons (KRS), both complete and not complete, which can be Kähler immersed into infinite-dimensional complex space forms. This shows that the triviality of a KRS induced by a finite-dimensional complex space form proved by Loi and Mossa (Proc. Amer. Math. Soc. 149:11 (2020), 4931–4941) does not hold when the ambient space is allowed to be infinite-dimensional. Moreover, we show that the radial potential of a radial KRS induced by a nonelliptic complex space form is necessarily defined at the origin
A characterization of complex space forms via Laplace operators
Inspired by the work of Lu and Tian (Duke Math J 125(2):351–387, 2004), in this paper we address the problem of studying those Kähler manifolds satisfying the Δ -property, i.e. such that on a neighborhood of each of its points the kth power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k (see below for its definition). We prove two results: (1) if a Kähler manifold satisfies the Δ -property then its curvature tensor is parallel; (2) if an Hermitian symmetric space of classical type satisfies the Δ -property then it is a complex space form (namely it has constant holomorphic sectional curvature). In view of these results we believe that if a Kähler manifold satisfies the Δ -property then it is a complex space form
Extremal Kähler Metrics Induced by Finite or Infinite-Dimensional Complex Space Forms
In this paper, we address the problem of studying those complex manifolds M equipped with extremal metrics g induced by finite or infinite-dimensional complex space forms. We prove that when g is assumed to be radial and the ambient space is finite-dimensional, then (M, g) is itself a complex space form. We extend this result to the infinite-dimensional setting by imposing the strongest assumption that the metric g has constant scalar curvature and is well behaved (see Definition 1 in the Introduction). Finally, we analyze the radial Kähler–Einstein metrics induced by infinite-dimensional elliptic complex space forms and we show that if such a metric is assumed to satisfy a stability condition then it is forced to have constant nonpositive holomorphic sectional curvature
On the third coefficient of TYZ expansion for radial scalar flat metrics
We classify radial scalar flat metrics with constant third coefficient of its TYZ expansion. As a byproduct of our analysis we provide a characterization of Simanca's scalar flat metric
Effective temperature of active matter
We follow the dynamics of an ensemble of interacting self-propelled motorized
particles in contact with an equilibrated thermal bath. We find that the
fluctuation-dissipation relation allows for the definition of an effective
temperature that is compatible with the results obtained using a tracer
particle as a thermometer. The effective temperature takes a value which is
higher than the temperature of the bath and it is continuously controlled by
the motor intensity
Limit Analysis of Strain Softening Frames Allowing for Geometric Nonlinearity
This paper extends classical limit analysis to account for strain softening and 2nd-order geometric nonlinearity simultaneously. The formulation is an instance of the challenging class of socalled (nonconvex) mathematical programs with equilibrium constraints (MPECs). A penalty algorithm is proposed to solve the MPEC. A practical frame example is provided to illustrate the approach
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