Related papers: Bochner-Kodaira Formulas and the Type IIA Flow

Following Le Jan and Watanabe we define a connection associated with a non-degenrrate diffusion operators. This connection is characterized here and shown to be the Levi-Civita connection for gradient systems. This both explains why such…

We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…

In this paper we construct a version of Ricci flow for noncommutative 2-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent results on the Gauss-Bonnet theorem for noncommutative…

We offer an example of the second order Kawaguchi metric function the extremal flow of which generalizes the flat space-time model of the semi-classical spinning particle to the framework of the pseudo-Riemannian space-time. The general…

Non-Abelian extensions of fluid dynamics, which can have applications to the quark-gluon plasma, are given. These theories are presented in a symplectic/Lagrangian formulation and involve a fluid generalization of the Kirillov-Kostant form…

We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…

In this note we classify some integrable invariant Sobolev metrics on the Abelian extension of the diffeomorphism group of the circle. We also derive a new two-component generalization of the Camassa-Holm equation. The system obtained…

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively…

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…

Properties of Hamiltonian symmetry flows on hyperbolic Euler-type Liouvillean equations E' are analyzed. Description of their Noether symmetries assigned to the integrals for these equations is obtained. The integrals provide Miura…

We introduce a framework for Newton's flows in probability space with information metrics, named information Newton's flows. Here two information metrics are considered, including both the Fisher-Rao metric and the Wasserstein-2 metric. A…

This paper is a review on recently found connection between geodesically equivalent metrics and integrable geodesic flows. Suppose two different metrics on one manifold have the same geodesics. We show that then the geodesic flows of these…

Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…

We improve the understanding of both finite time and infinite time singularities of the modified K\"ahler-Ricci flow as initiated by the second author of this paper in [26]. This is done by relating the modified K\"ahler-Ricci flow with the…

In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this…

We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of such metrics. We show that these metrics have certain…

A one-parameter family of coupled flows depending on a parameter $\kappa>0$ is introduced which reduces when $\kappa=1$ to the coupled flow of a metric $\omega$ with a $(1,1)$-form $\alpha$ due recently to Y. Li, Y. Yuan, and Y. Zhang. It…

We study average flow properties in porous media using a two-dimensional network simulator. It models the dynamics of two-phase immiscible bulk flow where film flow can be neglected. The boundary conditions are biperiodic which provide a…

We introduce a new geometric flow of Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. The flow depends on the choice of a background metric, it always reduces to a scalar equation…

We study flows of $G_2$-structures guided by the principle of dimensional reduction: natural geometric flows in $G_2$-geometry reduce to natural flows in complex geometry. Our main examples are the $G_2$-Laplacian coflow, which lifts the…