On the Pontrjagin classes of spray manifolds.

Shen, Zhongmin; Zhao, Runzhong

The characterization of projectively flat Finsler metrics on an open subset in $R^n$ is the Hilbert's fourth problem in the regular case. Locally projectively flat Finsler manifolds form an important class of Finsler manifolds. Every Finsler metric induces a spray on the manifold via geodesics. Therefore, it is a natural problem to investigate the geometric and topological properties of manifolds equipped with a spray. In this paper, we study the Pontrjagin classes of a manifold equipped with a locally projectively flat spray and show that such manifold must have zero Pontrjagin classes.

ISOPERIMETRICAL problems; GEOMETRY; ISOPERIMETRIC inequalities; MATHEMATICAL inequalities; PLANE geometry

Canadian Mathematical Bulletin, 2024, Vol 67, Issue 3, p544

0008-4395

Academic Journal

10.4153/S0008439523000954