Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 341–365 | Cite as

Lagrangian Grassmann manifold Λ(2)

Research Article


Based on the relationship between symplectic group Sp(2) and Λ(2), we provide an intuitive explanation (model) of the 3-dimensional Lagrangian Grassmann manifold Λ(2), the singular cycles of Λ(2), and the special Lagrangian Grassmann manifold SΛ(2). Under this model, we give a formula of the rotation paths dened by Arnold.


Lagrangian Grassmann manifold Lagrangian plane geometric representation singular cycle 


51H20 55R25 57M50 57N10 


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The author is grateful to Professor Yiming Long for his interest and Professor Xijun Hu for many useful advises and patient guidance. Also, the author would like to convey thanks to the anonymous referees for useful comments and suggestions. Finally, the author won’t forget his beloved friends and family members, for their understanding and endless love through the duration of his studies. This work was partially supported by the National Natural Science Foundation of China (Grant No. 11425105).


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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShandong UniversityJinanChina

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