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。

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.

1 Introduction 3
2 Pseudohermitian manifold 4
3 The Heisenberg group H2 5
4 Cartan’s method 6
4.1 The group representation of PSH(n) . . . . . . . . . . . . . . . . . . 6
5 Pseudohermitian submanifolds of H2 7
5.1 The Darboux frame for pseudohermitian submanifolds. . . . . . . . . 8
5.2 The fundamental vector field ν . . . . . . . . . . . . . . . . . . . . . 8
5.3 Intergrability condition . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.4 The structure equations . . . . . . . . . . . . . . . . . . . . . . . . 9
6 Main theorem 10

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