二維海森堡群上擬埃爾米特子流行的基本定理

The Fundamental Theorem of Pseudohermitian Submanifolds on 2 -Dimensional Heisenberg Groups

方齊佑(Chi-You Fang)

指導教授 ： 邱鴻麟

國立清華大學/理學院/數學系/碩士(2020年)

摘要

在這篇文章中主要的結果是去證明在二維海森堡群上垂直擬埃爾米特子流
行的不變量可以由其擬埃爾米特結構確定，所以有著相同埃爾米特結構的
垂直擬埃爾米特子流行之間最多差一個海森堡群上的鋼體運動。第二個結
果是擬埃爾米特流行嵌入二維海森堡群的條件，當然這種嵌入是唯一的。

關鍵字

海森堡群 ； 擬埃爾米特子流形 ； 基本定理

並列摘要

The main result of this thesis is to prove that the completely invariant of the vertical pseudohermitian submanifolds in Heisenberg group H2 can be determine by
the pseudohermitian structure. So two vertical pseudohermitian manifolds which
have the same pseudohermitian structure at most differ by a Heisenberg rigid motion. And the second result is the condition that a pseudohermitian manifold can
be embedded in the H2, of course that the embedding is unique in the sense that
they are the same after a Heisenberg rigid motion.

並列關鍵字

Heisenber group ； pseudohermitian submanifolds ； Fundamental theorem

參考文獻

[1] Ivey, T.A., Landsberg, J.M.: Cartan for beginners: differential geometry via moving

frames and exterior differential systems. Graduate Studies in Mathematics, vol. 61.

American Mathematical Society,

Providence, RI (2003)

[2] Lee, J.M.: The Fefferman metric and pseudohermitian invariants. Trans. Am. Math.