【摘要】 <正>如所知,在笛卡儿直交坐标系下,平坦黎曼空间的第二类Christoffel记号(即联络系数,以下简称克氏记号)全部是零。以下我们考虑非平坦的黎曼空间曾经考虑,在适当坐标系下第二类克氏记号都是常数的黎曼空间V_n,称为带有常数克氏记号的黎曼空间,简称为常数联络黎曼空间。他的研究仅限于V_n的基本度量形式更多还原

【Abstract】 A non-flat Riemannian space Vn is called Riemannian space with constant connection if its Christoffel symbols of the second kind are constant in some coordinate system {xi}. Following G. Vranceanu [3], a Riemannian space Vn with constant connection is said to be of genus p, if the components of the fundamental tensor in the coordinate system {xi} can be written in the form where cija are constant, and p is least.In this paper we prove the followingTheorem. Vn is a Riemannian space with constant connection of genus 2, if and only if its fundamental form (1,1) is reducible to the form (2.7) (2.18)or (2.20)It is also shown that the example of a Riemannian space with constant connection of genus 2 provided by G. Vranceanu [3] is actually of genus 1.更多还原