Ruslan Sharipov
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Formula for the force field of Newtonian dynamical systems admitting the normal shift of hypersurfaces in Riemannian manifolds is considered. Problem of globalization for geometric structures associated with this formula is studied.
In this article we obtain a classification of strictly locally convex affine hypersurfaces in A^{n+1} for which the geometrical structure is pointwise invariant under the group SO(n-1) represented by rotations around a fixed axis in the tangent space.
We study constant mean curvature spacelike hypersurfaces and in particular maximal hypersurfaces immersed in pp-wave spacetimes satisfying the timelike convergence condition. We prove the non-existence of compact spacelike hypersurfaces whose constant mean curvature is non-zero and also that every compact maximal hypersurface is totally geodesic. Moreover, we give an extension of the classical Calabi-Bernstein theorem to this class of pp-wave spacetimes.
We prove that a Riemannian product of type M x R (where R denotes the Euclidean line) admits totally umbilical hypersurfaces if and only if M has locally the structure of a warped product and we give a complete description of the totally umbilical hypersurfaces in this case. Moreover, we give a necessary and sufficient condition under which a Riemannian three-manifold carrying a unit Killing field admits totally geodesic surfaces and we study local and global properties of three-manifolds satisfying this condition.
An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. In this paper, we deal with positive definite affine hypersurfaces of dimension three. First we solve an algebraic problem. We determine the non-trivial stabilizers G of the pair (K,S) under the action of SO(3) on an Euclidean vectorspace (V,h) and find a representative (canonical form of K and S) of each (SO(3)/G)-orbit. Then, we classify hypersurfaces a…
In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every point there exists a linear transformation preserving the affine metric, the affine shape operator and the difference tensor K. The study of submanifolds which admit pointwise isometries was initiated by Bryant (math.DG/0007128). In this paper, we consider the 3-dimensional positive definite hypersurfaces for which at each point the group of symmetries is isom…
The isoperimetric problem in the Riemannian manifold admitting a non-trivial conformal vector field
本文在具有非平凡共形向量场的黎曼流形中引入保体积、降面积的平均曲率型流，证明其长时间存在与收敛，并建立星形区域等周不等式。
Class of Newtonian dynamical systems admitting normal blow-up of points in Riemannian manifolds is considered. Geometric interpretation for weak normality condition, which arose earlier in the theory of dynamical systems admitting the normal shift of hypersurfaces, is found.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton equations being special case for Newton's equations. In simplest cases (e. g. light propagation in isotropic non-homogeneous refracting media) the dynamics of points preserves orthogonality of wave front and rays. This property was generalized in the theory of dynamical systems ad…
Null hypersurface data and ambient vector fields: Killing horizons of order zero/one
本文研究带切向零向量场 η 的零超曲面，建立其形变张量与几何张量的恒等式，推广表面引力并提出三类抽象视界，涵盖一般拓扑与不动点情形。
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.
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.
Consider an area minimizing current modulo $p$ of dimension $m$ in a smooth Riemannian manifold of dimension $m+1$. We prove that its interior singular set is, up to a relatively closed set of dimension at most $m-2$, a $C^{1,α}$ submanifold of dimension $m-1$ at which, locally, $N\leq p$ regular sheets of the current join transversally, each sheet counted with a positive multiplicity $k_i$ so that $\sum_i k_i = p$. This completes the analysis of the structure of the singular set of area minimizing hypersurfaces modulo $p$, initiated by J. Taylor for $m=2$ and $p=3$ and extended by the authors…
A Structure Theory for Stable Codimension 1 Integral Varifolds with Applications to Area Minimising Hypersurfaces mod p
本文建立无低密度经典奇点的稳定余维1平稳积分varifold的结构理论，并用于刻画模p面积极小超曲面在平面切锥点附近的唯一性与广义$C^{1,\alpha}$分支结构。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。