簡易檢索 / 詳目顯示

回結果列表
研究生： 陳宗輝
Chung-Hwi Chen
論文名稱： The Euler Characteristic And Index Theory On Surfaces
曲面上尤拉特徵數及指標理論
指導教授： 張樹城
Shu-Cheng Chang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2008
畢業學年度： 96
語文別： 英文
論文頁數： 27
中文關鍵詞： 曲面指標 、由拉特徵數
相關次數： 點閱：1  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • Abstract
    In this thesis we will introduce two kind of indices on the surfaces . One of these indices measures the singularities of vector …field on surfaces , another reveals the structure of surfaces . Although it seems that these definition of indices are different , we will see that they closely relate to the Euler characteristic , a number which is invariant under topological transformation . Poincaré-Hopf Theorem is known as this essential property .

    Content Abstract 1.Introduction Part 1 . The index of vector field on surfaces 2.The relation between the index and Euler Characteristic Part 2 The 2nd kind of index on surfaces 3.Every compact differentiable manifold have a function with nondegenerate critical points 4.Every compact differentiable manifold has the same Homotopoy type with CW-complex 5.The calculation of Euler Characteristic Number 6.The relation between the 2nd kind of index and Euler Characteristic References

    References
    [1] Marvin J. Greenberg and John R. Harper. Algebraic Topology, chapter 2,pages 82-90. Benjamin/Cummings Publishing Company, 1981.
    [2] John W. Milnor. Topology From The Differentiable Viewpoit. The University Press Of Virginia Charlottesville, 1965.
    [3] John W. Milnor. Morse Theory. Princeton University Press, 1968.
    [4] James R. Munkery. Topology, chapter 4, pages 224-227. Prentice Hall, 2000.
    [5] James R. Munkery. Topology, chapter 2, page 147. Prentice Hall, 2nd edition, 2000.
    [6] Barrett O’Nell. Elementary Di¤erential Geometry, chapter 7, pages 351-361.Harcourt Academic Press, 2nd edition, 1997.

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)
    全文公開日期 本全文未授權公開 (國家圖書館：臺灣博碩士論文系統)
    QR CODE