指数不齐次处理下保持两向量夹角的Finsler联络
Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatment
摘要：
证明了切黎曼空间共形平坦的Finsler空间的特征是其指标线是常曲率常曲率空间。在这样的空间中，芬斯勒规范化的两向量角可以从相应的黎曼空间的两向量角中得到解释。因此，即使在指标不均匀的水平上，也就是说，当指标曲率值${\mathcal C}_{\text{Ind.}} $被允许是指标位置点$x$的任意光滑函数时，明确提出保持角度的连接的方式是开放的。所得到的连接是度量的，其偏转部分与进入等式${\mathcal C}_{\text{Ind.}} \equiv H^2.$的函数$H(x)$的梯度成比例。利用协变导数的传递性，从共变导数的传递子中，得到了相应的曲率张量，并得到了各种有用的表示。Finsleroid空间已经被明确地描绘出来了。
英文摘要：
The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be explicated from the respective two-vector angle of the associated Riemannian space. Therefore the way is opening to propose explicitly the connection preserving the angle even at the indicatrix-inhomogeneous level, that is, when the indicatrix curvature value ${\mathcal C}_{\text{Ind.}} $ is permitted to be an arbitrary smooth function of the indicatrix position point $x$. The connection obtained is metrical with the deflection part which is proportional to the gradient of the function $H(x)$ entering the equality ${\mathcal C}_{\text{Ind.}} \equiv H^2.$ Also the connection is covariant-constant. When the transitivity of covariant derivative is used, from the commutators of covariant derivatives the associated curvature tensor is found. Various useful representations have been developed. The Finsleroid space has been explicitly outlined.
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