臺灣博碩士論文加值系統

在此，利用斯托克斯定理建立一個在海森堡群上，類比黎曼流形上的散度定理。

In this thesis, we use the Stokes’ theorem to establish a subdivergence
theorem for the Heisenberg groups which is analogue of the divergence theorem on
Riemannian manifolds.

Introduction 1
Chapter 1. Preliminaries 3
1. Heisenberg groups 3
2. Contact bundle with a complex structure 4
3. Hermitian structure 5
Chapter 2. Subdivergence theorem on Heisenberg groups 9
1. Complex version 9
2. Real version 11
Bibliography 15

Chiu, Hung-Lin, Singularities and some invariants of singularities in contact 3-manifolds, Taiwanese Journal of Mathematics 10 , no. 5, 1391–1408, The Mathematical Society of the Republic of China, Taipei, 2006.
L. Capogna, D. Danielli, S. D. Pauls, J. T. Tyson, An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem, Progr. Math., 259, Birkhäuser, Basel, 2007.
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 8th ed., Springer, New York, 1997.
Yozo Matsushima, Differentiable Manifolds, Marcel Dekker, Inc., New York, 1972.