On the Jacobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres. III
On the Jacobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres. III
复制标题
与对称空间到球体的最小等距浸没相关的雅可比微分算子。
DOI：
10.18910/5349
复制
发表时间：
1982
影响因子：
0.4
通讯作者：
T. Nagura
中科院分区：
文献类型：
--
作者：
T. Nagura
式中，E表示{Ft}的无穷小正态变化(见第1节)。雅可比微分算子S是自伴的强椭圆算子。因此，F的指数和零性是从S的谱得到的。这里的指数和零性定义为M到M的模微分同构的浸入空间上的体积积分在F处的Hessian指数和零性。对于极小等距浸入的研究，研究S及其谱似乎是很重要的。长谷川[4]研究极小子流形的谱几何。设M是紧对称空间，M是单位球面，F是等变空间
where E denotes the infinitesimal normal variation of {Ft} (see section 1). The Jacobi differential operator S is self-adjoint and strongly elliptic. Therefore the index and the nullity of F are obtained from the spectra of S. Here the index and the nullity are defined as those of the Hessian at F of the volume integral on the space of immersions of M into M modulo diffeomorphisms of M. For the study of minimal isometric immersions it seems to be important to study S and its spectra.* However there have been few studies on these problems except for the recent works of Hasegawa and others. Hasegawa [4] studies the spectral geometry of minimal submanifolds. Let M be a compact symmetric space, M a unit sphere, and F an equivariant