a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

We study semi-Riemannian submanifolds of arbitrary codimension in a Lie group [Formula: see text] equipped with bi-invariant metric. In particular, we show that, if the normal bundle is closed under bracket, then any Jacobi operator equals square associated invariant shape text]. This permits to understand curvature adaptedness geometrically, terms left translations. For example, case where Rie...

We study the dynamics of magnetic flows on Heisenberg groups, investigating extent to which properties underlying Riemannian geometry are reflected in flow. Much analysis, including a calculation Mañé critical value, is carried out for $$(2n+1)$$ -dimensional groups endowed with any left invariant metric and exact, left-invariant field. In three-dimensional case, we obtain complete analysis lef...

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

A new approach to error analysis is introduced, based on the observation that many numerical procedures can be interpreted as computations of products in a suitable Lie group. The absence of an additive error law for such procedures is intimately related to the nonexistence of bi-invariant metrics on the relevant groups. Introducing the notion of an almost Inn(G) invariant metric (a left invari...

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamilton...

We discuss the geometry of homogeneous Ricci solitons. After showing the nonexistence of compact homogeneous and noncompact steady homogeneous solitons, we concentrate on the study of left invariant Ricci solitons. We show that, in the unimodular case, the Ricci soliton equation does not admit solutions in the set of left invariant vector fields. We prove that a left invariant soliton of gradie...

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...