论文标题
关于$ m $ $ -Kropina空间的Metrionable of null 1form
On the metrizability of $m$-Kropina spaces with closed null 1-form
论文作者
论文摘要
我们研究了Finsler空间的局部METRININIS，其$ M $ -Kropina度量$ f =α^{1+m}β^{ - m} $，其中$β$是封闭的null 1型。我们表明，只有当（伪）Riemannian Metric $α$和1型$β$在某些坐标中具有非常特异性的形式时，这种空间是Berwald类型的。特别是，当$α$的签名是洛伦兹的时，$α$属于昆特类的某个子类，$β$会产生相应的无效一致性，并且这以自然的方式进行任意签名。我们使用此结果来证明这种$ M $ -Kropina空间上的仿射连接在且仅当Ricci张量构造的形式形式形式时，仿射连接是对称的。特别是，我们构建了Szabo的Metrrization定理的所有反例，该样本仅被证明是用于正定的正定鳍指标，这些指标在所有缝隙切线捆绑包上是规则的。
We investigate the local metrizability of Finsler spaces with $m$-Kropina metric $F = α^{1+m}β^{-m}$, where $β$ is a closed null 1-form. We show that such a space is of Berwald type if and only if the (pseudo-)Riemannian metric $α$ and 1-form $β$ have a very specific form in certain coordinates. In particular, when the signature of $α$ is Lorentzian, $α$ belongs to a certain subclass of the Kundt class and $β$ generates the corresponding null congruence, and this generalizes in a natural way to arbitrary signature. We use this result to prove that the affine connection on such an $m$-Kropina space is locally metrizable by a (pseudo-)Riemannian metric if and only if the Ricci tensor constructed form the affine connection is symmetric. In particular we construct all counterexamples of this type to Szabo's metrization theorem, which has only been proven for positive definite Finsler metrics that are regular on all of the slit tangent bundle.
