Certain minimal or homologically volume minimizing submanifolds in compact symmetric spaces
Certain minimal or homologically volume minimizing submanifolds in compact symmetric spaces
复制标题
紧凑对称空间中的某些最小或同调体积最小化子流形
DOI：
10.21099/tkbjm/1496160196
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发表时间：
1985
影响因子：
0.7
通讯作者：
H. Tasaki
中科院分区：
文献类型：
--
作者：
H. Tasaki
本文主要研究紧致对称空间中的极小子流形、紧致单李群中的同调体积极小子流形和四元Kahler流形。第一个问题是通过计算子流形的第二基本形式来研究的。第二节利用紧致对称空间的第一共轭轨迹的结构定理（Takeuchi [5]），计算了紧致对称空间的第一共轭轨迹中开稠密的子流形的第二基本形式，证明了它的极小性，并证明了该子流形没有测地点。第二个问题是利用Harvey和Lawson [2]提出的“校准”概念来研究的。这个概念在第3节和第4节中使用。Kahler流形的基本2-形式是标定的重要例子之一。它满足Wirtinger不等式，可以表述如下。设M是具有基本2-形式的Kahler流形。然后
In thispaper we shall study minimal submanifolds in compact symmetric spaces and homologically volume minimizing submanifolds in compact simple Lie groups and quanternionic Kahler manifolds. The firstsubjectis studied by computing the second fundamental forms of submanifolds. In Section 2 using the structure theorem of the firstconjugate loci of compact symmetric spaces (Takeuchi [5])we compute the second fundamental form of a certainsubmanifold which is open and dense in the firstconjugate locus of a compact symmetric space and prove the minimality of it. Moreover we show that the submanifold has no geodesic point. The second subjectis studied by using the notion "calibration" introduced by Harvey and Lawson [2]. This notionisused in Sections 3 and 4. The fundamental 2-form of a Kahler manifold is one of important examples of calibrations. It satisfiesWirtinger's inequality, which can be statedas follows. Let M be a Kahler manifold with fundamental 2-form o). Then