In this paper, we consider the relation of the Morse index of a closedgeodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closedgeodesic c on a Riemannian manifold M with its lin...In this paper, we consider the relation of the Morse index of a closedgeodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closedgeodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), weconstruct a symplectic path γ(t) starting from identity I and ending at P, such that the Morseindex of the closed geodesic c equals the Maslov-type index of γ. As an application of this result,we study the parity of the Morse index of any closed geodesic.展开更多
基金Project 10071040 supported by NNSF,200014 supported by Excellent.Ph.D.Funds of ME of ChinaPMC Key Lab.of ME of China
文摘In this paper, we consider the relation of the Morse index of a closedgeodesic with the Maslov-type index of a path in a symplectic group. More precisely, for a closedgeodesic c on a Riemannian manifold M with its linear Poincare map P (a symplectic matrix), weconstruct a symplectic path γ(t) starting from identity I and ending at P, such that the Morseindex of the closed geodesic c equals the Maslov-type index of γ. As an application of this result,we study the parity of the Morse index of any closed geodesic.
