论文标题
带有偏斜循环结构的Riemannian歧管和相关的当地同条Kähler歧管
A Riemannian manifold with skew-circulant structures and an associated locally conformal Kähler manifold
论文作者
论文摘要
考虑了一个四维的Riemannian歧管M，配备了额外的张量结构s，其第四个功率是减去身份。结构s在M上的某个点的某个点的某个基础上具有偏斜的循环矩阵。基本张量是通过g在如此的多种歧管（M，G，S）上定义的，并且由S的协方差衍生物定义。这种张量满足了一个特征性的身份，这对于通常的保形转换而言是不变的。获得（M，G，S）的某些曲率特性。构建了一个谎言组作为所考虑的类型的多种形式。还考虑了与（m，g，s）相关的Hermitian歧管。事实证明，这是当地的保质kähler歧管。
A 4-dimensional Riemannian manifold M, equipped with an additional tensor structure S, whose fourth power is minus identity, is considered. The structure S has a skew-circulant matrix with respect to some basis of the tangent space at a point on M. Moreover, S acts as an isometry with respect to the metric g. A fundamental tensor is defined on such a manifold (M,g,S) by g and by the covariant derivative of S. This tensor satisfies a characteristic identity which is invariant to the usual conformal transformation. Some curvature properties of (M,g,S) are obtained. A Lie group as a manifold of the considered type is constructed. A Hermitian manifold associated with (M,g,S) is also considered. It turns out that it is a locally conformal Kähler manifold.
