复射影空间中拟全实极小子流形的谱几何

J4 ›› 2010, Vol. 48 ›› Issue (1): 15-21.

复射影空间中拟全实极小子流形的谱几何

尹松庭¹, 宋卫东²

1. 铜陵学院数学计算机系, 安徽铜陵 244000|2. 安徽师范大学数学计算机科学学院, |安徽芜湖 241000

收稿日期:2009-01-19 出版日期:2010-01-26 发布日期:2010-01-27
通讯作者: 宋卫东 E-mail:swd56@sina.com.

Spactral Geometry of QuasiTotally Real Minimal Submanifoldsin a Complex Projective Space

YIN Songting¹, SONG Weidong²

1. Department of Mathematics and Computer Science, Tongling College, Tongling 244000, Anhui Province, China;
2. College of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, Anhui Province, China

Received:2009-01-19 Online:2010-01-26 Published:2010-01-27
Contact: SONG Weidong E-mail:swd56@sina.com.

摘要/Abstract

摘要：

研究复射影空间中拟全实极小子流形的谱几何, 利用活动标架法并通过计算平均曲率向量的Laplacian, 建立了仅与子流形内蕴几何量有关的特征值不等式, 将相关结果推广到复射影空间中的一般子流形上, 并获得了拟全实极小子流形存在u阶浸入的充要条件.

关键词: 复射影空间, 拟全实, 极小子流形, 谱几何, 特征值不等式

Abstract:

The authors studied the spactral geometry of quasitotally real minimal submanifolds in a complex projective space. By means of the method of moving frames and caculating Laplacian of the mean curvature vector, the eigenvalue inequality for the submanifolds which only related to intrinsic geometric quality was established. This result generated correlation theorms to generic submanifolds in a complex projective space. Moreover, the authors also got one necessary and sufficient condition on uorder immersion of quasitotally real minimal submanifolds.

Key words: complex projective space, quasitotally real, minimal submanifolds, spactral geometry, eigenvalue inequalities

中图分类号:

O186

尹松庭, 宋卫东. 复射影空间中拟全实极小子流形的谱几何[J]. J4, 2010, 48(1): 15-21.

YIN Song-Ting, SONG Wei-Dong. Spactral Geometry of QuasiTotally Real Minimal Submanifoldsin a Complex Projective Space[J]. J4, 2010, 48(1): 15-21.

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