Related papers: Homogeneous spinor flow
We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor $\psi$ of algebraic type $F \cdot \psi = 0$ with respect to the unique connection $\nabla$ preserving the quasi-Sasakian structure and…
We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.
In this paper, we study transversely holomorphic partially hyperbolic flows, i.e. those whose holonomy pseudo-group is given by biholomorphic maps. We prove in the seven-dimensional case that under the assumption that the subcenter…
These notes record three lectures given at the workshop "Higher symmetries in Physics", held at the Universidad Complutense de Madrid in November 2008. In them we explain how to construct a Lie (super)algebra associated to a spin manifold,…
This is a continuation of the research in [16]. Let $(\overline{M},g_{-1})$ be a closed geodesic $r_0$-ball in the hyperbolic space $(\mathbb{H}^n,g_{-1})$. Let $m\neq1$ be a positive constant. In this paper, we show that for $n\geq3$,…
A hypersymplectic structure on a 4-manifold is a triple $\omega_1, \omega_2, \omega_3$ of 2-forms for which every non-trivial linear combination $a^1\omega_1 + a^2 \omega_2 + a^3 \omega_3$ is a symplectic form. Donaldson has conjectured…
We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the…
The dynamics of straight line flows on compact half-translation surfaces (surfaces formed by gluing Euclidean polygons edge-to-edge via translations possibly composed with rotation by $\pi$) has been widely studied due to their connections…
We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.
We give a classification of homogeneous Riemannian structures on (non locally symmetric) $3$-dimensional Lie groups equipped with left invariant Riemannian metrics. This work together with classifications due to previous works yields a…
We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat solvsoliton, which is independent of the initial left-invariant metric. As an application,…
This paper investigates the nature of the development of two-dimensional steady flow of an incompressible fluid at the rear stagnation-point.
We introduce a combinatorial curvature flow for PL metrics on compact triangulated 3-manifolds with boundary consisting of surfaces of negative Euler characteristic. The flow tends to find the complete hyperbolic metric with totally…
The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the inhomogeneous Dirac equation. The main idea leading to the description of a surface M^2 by a spinor field is the observation…
We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and…
In this paper, we prove that in the system of bending flows on the moduli space of polygons with fixed side lengths introduced by Kapovich and Millson, the singular fibers are isotropic homogeneous submanifolds. The proof covers the case…
Given a $C^{1+\beta}$ flow $\varphi$ with positive speed on a closed smooth Riemannian manifold, we code two homoclinically related $\varphi$-invariant probabilities by an irreducible countable topological Markov flow. As an application, we…
In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of…
We study the streamlines of $\infty$-harmonic functions in planar convex rings. We include convex polygons. The points where streamlines can meet are characterized: they lie on certain curves. The gradient has constant norm along…