Title：Inverse problem of sprays with scalar curvature

Speaker：莫小欢  （北京大学）

Time：2019年6月29日     下午 16:00-17:00

Room：东区管理科研楼  0029cc金沙贵宾会1418室

Abstract：Every Finsler metric on a differential manifold induces a spray. The converse is not true. Therefore it is one of the most fundamental problems in spray geometry to determine whether a spray is induced by a Finsler metric which is regular, but not necessary positive definite. This problem is called  inverse problem. In this lecture we discuss inverse problem of sprays with scalar curvature. In particular, we show that if such a spray G on a manifold is of vanishing H-curvature, but G has not isotropic curvature, then G is not induced by any (not necessary positive definite) Finsler metric. We also find infinitely many sprays on an open domain U in R^n with scalar curvature and vanishing H-curvature, but these sprays have no isotropic curvature. This contrasts sharply with the situation in Finsler geometry.