Results 1 to 10 of about 1,451 (107)
Deformation classes in generalized Kähler geometry
Complex Manifolds, 2020 We describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry.
Gibson Matthew, Streets Jeffrey
doaj +1 more source
The commutative nonassociative algebra of metric curvature tensors
Forum of Mathematics, Sigma, 2021 The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative multiplications invariant with respect to the symmetric bilinear form determined by the metric ...
Daniel J. F. Fox
doaj +1 more source
Perelman's entropy for some families of canonical metrics [PDF]
, 2014 We numerically calculate Perelman’s entropy for a variety of canonical metrics on CP1-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics.
Bérard-Bergery [Bérard-Bergery 82] L. +1 more
core +2 more sources
The Soliton-Ricci Flow with variable volume forms
Complex Manifolds, 2016 We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previouswork.We still call this new flow, the ...
Pali Nefton
doaj +1 more source
Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties [PDF]
, 2012 We show, using a direct variational approach, that the second boundary value problem for the Monge-Amp\`ere equation in R^n with exponential non-linearity and target a convex body P is solvable iff 0 is the barycenter of P.
Berman, Robert J., Berndtsson, Bo
core +4 more sources
Calabi flow on toric varieties with bounded Sobolev constant, I
Complex Manifolds, 2016 Let (X, P) be a toric variety. In this note, we show that the C0-norm of the Calabi flow φ(t) on X is uniformly bounded in [0, T) if the Sobolev constant of φ(t) is uniformly bounded in [0, T).
Huang Hongnian
doaj +1 more source
Action-Amplitude Approach to Controlled Entropic Self-Organization
Entropy, 2014 Motivated by the notion of perceptual error, as a core concept of the perceptual control theory, we propose an action-amplitude model for controlled entropic self-organization (CESO).
Vladimir Ivancevic +2 more
doaj +1 more source
On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows
, 2020 Let $X$ be a compact K\"ahler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a K\"ahler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus Donaldson ...
Xia, Mingchen
core +2 more sources
CANONICAL MEASURES AND KÄHLER-RICCI FLOW [PDF]
, 2012 We show that the Kähler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model.
Gang Tian, Jian Song
core +1 more source
Kähler metrics via Lorentzian Geometry in dimension four
Complex Manifolds, 2019 Given a semi-Riemannian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics gK is constructed, defined on an open set in M, which ...
Aazami Amir Babak, Maschler Gideon
doaj +1 more source