Totally real minimal 2-spheres in quaternionic projective space

作     者：HE Yijun WANG Changping 

作者机构：LMAM School of Mathematical Sciences Peking University Beijing 100871 China LMAM School of Mathematical Sciences Peking University Beijing 100871 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2005年第48卷第3期

页      面：341-349页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：Acknowledgements We would like to thank Mr.Ma Xiang for his helpful discussion.This work was supported by RFDP,Qiushi Award,973 Project Jiechu Grant of NSFC. 

主　　题：quaternionic projective space, totally real surfaces, minimal surfaces. 

摘      要：Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J,K} of complex structures on HPn satisfying IJ = -JI = K, JK = -KJ = I, KI = -IK = J. A surface M HPn is called totally real, if at each point p ∈ M the tangent plane TpM is perpendicular to I(TpM),J(TpM) and K(TpM). It is known that any surface M RPn HPn is totally real, where RPn HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don t come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in RP2m RPn HPn with 2m ≤ n. As a consequence we show that the Veronese sequences in RP2m (m ≥ 1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.