Dynamical systems admitting the normal shift

Normal forms of two-dimensional metrics admitting exactly one essential projective vector field

We give a complete list of mutually non-diffeomorphic normal forms for the two-dimensional metrics that admit one essential (i.e., non-homothetic) projective vector field. This revises a result from the literature and extends the results of two papers, by R.L. Bryant & G. Manno & V.S. Matveev (2008) and V.S. Matveev (2012) respectively, solving a problem posed by Sophus Lie in 1882.

A non-normal Fefferman-type construction of split-signature conformal structures admitting twistor spinors

We treat a non-normal Fefferman-type construction based on an inclusion $\SL(n+1)\embed\Spin(n+1,n+1)$. The construction associates a split signature $(n,n)$-conformal spin structure to a projective structure of dimension $n$. For $n\geq 3$ the induced conformal Cartan connection is shown to be normal if and only if it is flat. The main technical work of this article consists in showing that in the non-flat case the normalised conformal Cartan connection still allows a parallel (pure) spin-tractor and thus a corresponding (pure) twistor spinor on the conformal space. The Fefferman-type constru…

On the concept of normal shift in non-metric geometry

Theory of Newtonian dynamical systems admitting normal shift of hypersurfaces was first developed for the case of Riemannian manifolds. Recently it was generalized for manifolds geometric equipment of which is given by some regular Lagrangian or, equivalently, by some regular Hamiltonian dynamical system. In present paper we consider further generalization of this theory for the case, when geometry of manifold is given by generalized Legendre transformation.

On manifolds with holomorphic normal projective connections

The authors give a complete classification of projective threefolds admitting a holomorphic normal projective connection. Moreover, they prove a general structure theorem on complex projective manifolds admitting a holomorphic normal projective connection, saying in particular, that any such manifold is either the projective space or minimal in the sense of Mori.

带对称性的双切触结构：局部正规形式

Bi-contact structures with symmetry: local normal forms

本文研究三维流形上带单参数对称的横截双切触分布的局部正规形式，发现可定向Anosov流可由具极大局部对称性的反向切触分布对的交整体表示。

Newtonian normal shift in multidimensional Riemannian geometry

Explicit description for arbitrary Newtonian dynamical system admitting the normal shift in Riemannian manifold of the dimension $n\geq 3$ is found. On the base of this result the kinematics of normal shift of hypersurfaces along trajectories of such system is studied.

Normal shift in general Lagrangian dynamics

It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of constant phase, their points move along lines which are called rays. In non-homogeneous anisotropic media rays are not straight lines. Their shape is determined by modified Lagrange equations. An important observation is that for most usual cases propagating wave fronts are perpendicular to rays in the sense of some Riemannian metric. This happens when Lagrange fun…

李奇内茨型结果在实秩至少为3的抛物几何中的失效

Failure of Lichnerowicz-type result in parabolic geometries of real rank at least $3$

该研究通过非刚性抛物几何构造了非平坦的Cartan几何，推翻了李奇内茨型猜想在实秩至少为3的模型几何中的有效性。

Dynamical systems accepting the normal shift on an arbitrary Riemannian manifold

Newtonian dynamical systems which accept the normal shift on an arbitrary Riemannian manifold are considered. For them the determinating equations making the weak normality condition are derived. The expansion for the algebra of tensor fields is constructed.