A study on a generating function of a complex Lagrangian submanifold and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540103
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Meijo University
• Principal Investigator: EJIRI Norio 名城大学, 理工学部, 教授 (80145656)
• Co-Investigator(Renkei-kenkyūsha): OZAWA Tetuya 名城大学, 理工学部, 教授 (20169288) ; HASHIMOTO Hideya 名城大学, 理工学部, 教授 (60218419)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 複素ラグランジュ錐の生成関数 / 平坦トーラスの極小曲面 / 極小曲面の変形空間 / ヤコビ作用素 / index and nullity / null submanifold / horizontal submanifold / ruled submanifold

Outline of Final Research Achievements

We study a generating function of complex Lagrangian submanifold and get the relation with other submanifolds. In particular, by the relation between a generating function of a complex Lagrangian cone and a special pseudo kaehler structure, we obtain an algorithm to compute the index and the nullity of a compact, orientable, minimal surface in a torus by the periods of Abelian differentials of the first kind and the second kind. Concretely, we can seek the index and the nullity of Schwarz' P family, D family and H family.

Free Research Field

微分幾何学