Cartan connection of transversally Finsler foliation
The purpose of this paper is to define transversal Cartan connection of Finsler foliation and to prove its existence and uniqueness.
Parallelograms inscribed in a curve having a circle as π/2-isoptic
Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.
Cartan connection of transversally Finsler foliation
The purpose of this paper is to define transversal Cartan connectionof Finsler foliation and to prove its existence and uniqueness.
On the curves of constant relative width
Projective spaces of second order.
Grassmannians of higher order appeared for the first time in a paper of A. Szybiak in the context of the Cartan method of moving frame. In the present paper we consider a special case of higher order Grassmannian, the projective space of second order. We introduce the projective group of second order acting on this space, derive its Maurer-Cartan equations and show that our generalized projective space is a homogeneous space of this group.
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