论文标题
球体捆绑包的sasakian几何形状
Sasakian Geometry on Sphere Bundles
论文作者
论文摘要
本文的目的是研究奇数尺寸球体上的sasakian几何形状，捆绑在平滑的投射代数品种$ n $上，最终，但可能无法实现的目标，即了解极端和恒定标量曲线的存在和不存在的目标和不存在的目标。我们将Yamazaki \ Cite {Yam99}的纤维结构用于Sasaki案例。该结构取决于$ d+1 $ intectalkählerclass $ [ω_j] $ n $上不一定是kähler锥中的colinear的选择。我们表明，colinear案例等于\ cite {bg00a，bgo06}在\ cite {boto13，boto13，boto14a}中使用的不同连接构造的子类，当时是球形案例，当非彩色案件引起了新的不可分解的锥形sasaki sasaki接触CR的无限家族。我们证明，其中一些结构的Sasaki锥包含一组开放的极端Sasaki指标，并且对于某些专业情况，该锥体内的常规射线被证明具有恒定的标态曲率。我们还计算了Riemann表面产物上所有此类球体捆绑的共同体学组。
The purpose of this paper is to study the Sasakian geometry on odd dimensional sphere bundles over a smooth projective algebraic variety $N$ with the ultimate, but probably unachievable goal of understanding the existence and non-existence of extremal and constant scalar curvature Sasaki metrics. We apply the fiber join construction of Yamazaki \cite{Yam99} for K-contact manifolds to the Sasaki case. This construction depends on the choice of $d+1$ integral Kähler classes $[ω_j]$ on $N$ that are not necessarily colinear in the Kähler cone. We show that the colinear case is equivalent to a subclass of a different join construction orginally described in \cite{BG00a,BGO06}, applied to the spherical case by the authors in \cite{BoTo13,BoTo14a} when $d=1$, and known as cone decomposable \cite{BHLT16}. The non-colinear case gives rise to infinite families of new inequivalent cone indecomposable Sasaki contact CR on certain sphere bundles. We prove that the Sasaki cone for some of these structures contains an open set of extremal Sasaki metrics and, for certain specialized cases, the regular ray within this cone is shown to have constant scalar curvature. We also compute the cohomology groups of all such sphere bundles over a product of Riemann surfaces.
