Integrable smooth planar billiards and evolutes.
Integrable string models in terms of chiral invariants of groups.
Integrable systems and group actions
The main purpose of this paper is to present in a unified approach to different results concerning group actions and integrable systems in symplectic, Poisson and contact manifolds. Rigidity problems for integrable systems in these manifolds will be explored from this perspective.
Integral distance on a Lipschitz Riemannian manifold.
Integral formula for secantoptics and its application
Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieślak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results.
Integral formulae for a Riemannian manifold with two orthogonal distributions
We obtain a series of new integral formulae for a distribution of arbitrary codimension (and its orthogonal complement) given on a closed Riemannian manifold, which start from the formula by Walczak (1990) and generalize ones for foliations by several authors. For foliations on space forms our formulae reduce to the classical type formulae by Brito-Langevin-Rosenberg (1981) and Brito-Naveira (2000). The integral formulae involve the conullity tensor of a distribution, and certain components of the...
Integral formulas for closed spacelike hypersurfaces in anti-de Sitter space
In this paper, we study closed -maximal spacelike hypersurfaces in anti-de Sitter space with two distinct principal curvatures and give some integral formulas about these hypersurfaces.
Integral formulas for compact spacelike n-submanifolds in de Sitter spaces Applications to the parallel mean curvature vector case.
Integral formulas related to ovals.
Integral formulas related to wave fronts
In the first section of the paper we study some properties of oriented volumes of wave fronts propagating in spaces of constant curvature. In the second section, we generalize to an arbitrary isometric action of a Lie group on a Riemannian manifold the following principle: an extra pression inside of a ball does not move it.
Integral geometry and real zeros of Thue-Morse polynomials.
Integral geometry for complexes of rational curves
Integral Geometry of the action fof ST(3) on the space E...
Integral Inequalities for Maximal Space-like Submanifolds in the Indefinite Space Form
Integral inequalities for maximal space-like submanifolds in the indefinite space form.
Integral Invariants of Principal SO(n)(r)Grouv Structures on Space Forms.
Integral submanifolds with closed conformal vector field in Sasakian manifolds.
Integral transforms for divisors in and solutions of systems of PDE’s
Integrality of characteristic numbers on complete Kähler manifolds.
Integrals and variational multipliers of second-order ordinary differential equations
Summary: Here, a relation between integrals and variational multipliers of a system of second-order ordinary differential equations is studied. A simple necessary and sufficient local condition for the existence of a multiplier is given.