Ruled real surfaces formed by Kaehler magnetic fields

在研究黎曼流形时，测地线无疑是一个非常重要的对象。但是如果我们考虑所有光滑曲线的族，测地线族是一个小族。在这个原因中，首席研究员研究Kaehler流形通过调查Kaehler磁场的轨迹，这是Kaehler形式的常数倍1。比较定理为了研究可变全纯截面曲率的Kaehler流形，我们考虑由轨迹和扇形构成的直纹真实的曲面上的新月。在Kaehler流形截面曲率的假设下，我们可以通过复空间形式上相应物体的长度来估计这些物体的回路长度。2.复空间形式中测地球上Sasaki磁场的轨迹我们考虑奇维流形上的Sasaki磁场。这对应于真实的eavn维流形上的Kaehler磁场。虽然com中的测地球 ...更多信息 复空间形式是模型空间，Sasaki磁场轨迹的性质与复空间形式上Kaehler磁场轨迹的性质有很大不同。3.等距浸入刻画Kaehler流形通过等距浸入到真实的空间形式中来研究Kaehler流形。由于等距浸入给一些结构刚性流形上，我们认为家庭的曲线具有点的顺序2，其中包括家庭的轨迹Kaehler磁场。我们可以把被全脐浸入或第一标准嵌入浸入的复空间形式刻画为那些诱导映射保持2阶性质和曲率对数导数的复空间形式。如果我们把2阶性质的条件减弱到它们的外形状是2阶的条件，那么我们就可以刻划秩小于3的埃尔米特对称空间。

When we study Riemannian manifolds, it is needless to say that geodesics play quite important object. But if we consider the family of all smooth curves, the family of geodesics is a small family. In this reason the head investigator studied Kaehler manifolds by investigating trajectories for Kaehler magnetic fields, which are constant multiples of the Kaehler form1.Comparison theoremsIn order to study Kaehler manifolds of variable holomorphic sectional curvatures, we consider crescents on a ruled real surface formed by trajectory and trajectory-sectors. Under an assumption on sectional curvatures of a Kaehler manifold, we can estimate lengths of circuits of these objects by length of corresponding objects on a complex space form.2.Trajectories for Sasaki magnetic fields on geodesic spheres in a complex space formWe consider Sasaki magnetic fields on odd dimensional manifolds. This corresponds to Kaehler magnetic fields on real eavn dimensional manifolds. Though geodesic spheres in com … More plex space forms are model spaces, properties of trajectories for Sasaki magnetic fields are quite different from properties of trajectories for Kaehler magnetic fields on complex space forms. There are trajectories which have the same length but are not congruent to each other.3.Characterizations of some Kaehler manifolds through isometric immersionsWe study Kaehler manifolds through isometric immersions into real space forms. Since isometric immersions give some structural rigidity on manifolds, we consider the family of curves having points of order 2, which includes the family of trajectories for Kaehler magnetic fields. We can characterize complex space forms immersed by totally umbilic immersions or 1st standard embeddings as those whose induced maps preserve order 2 property and curvature logarithmic derivative. If we weaken the condition on order 2 property to the condition that their extrinsic shapes are of order 2, then we can characterize Hermitian symmetric spaces of rank less than 3 Less