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課程名稱 |
大域微分幾何
INTRODUCTION TO GLOBAL DIFFERENTIAL GEOMETRY |
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開課學期 |
97-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
黃武雄 |
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課號 |
MATH5313 |
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課程識別碼 |
221 U3760 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二3,4,@(10:20~) |
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上課地點 |
新404 |
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備註 |
總人數上限：60人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
以討論曲面的大域性質為主，兼亦提及高維流形的相關結果。課程內容包含像：ISOPERIMETRIC INEQUALITIES, HOPF-POINCARE INDEX THEOREM, HADAMARD’S THEOREM OF OVALOIDS, ALEXANDROV SYMMETRIZATION AND HOPF’S THEOREM OF GENUS ZERO, CONVEXITY PROBLEMS, CONGRUENCE THEOREMS, HYPERBOLIC SPACES, 等這些論題。 |
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課程目標 |
THE OBJECT OF DIFFERENTIAL GEOMETRY IS TO UNDERSTAND “CURVED SPACES” OF ARBITRARY DIMENSION. BUT MOST OF THE IDEAS AND THE TOOLS OF THE DISCIPLINE ARE ESSENTIALLY BASED ON TWO DIMENSIONAL SURFACES. THIS COURSE PROVIDES INSIGHT AND TECHNIQUES DEVELOPED IN CERTAIN IMPORTANT TOPICS ON GLOBAL SURFACES. SOME OF THEM ARE ALSO VALID FOR HIGHER DIMENSIONS, FOR EXAMPLE, ALEXANDROV’S SYMMETRIZATION AND HOPF-POINCARE INDEX THEOREM. REMARK THAT “GLOBAL” GEOMETRIC PROPERTIES ARE EMPHASIZED IN THE COURSE. |
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課程要求 |
COURSE PREREQUISITE：大三微分幾何（上學期）, GEOMETRY(FALL) COURSE FOR JUNIORS.
GRADING SCHEME：BASED ON STUDENT’S PERFORMANCE IN THE CLASS, THEIR HOME WORKS AND FINAL REPORTS.
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預期每週課後學習時數 |
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Office Hours |
每週二 13:00~15:00 |
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指定閱讀 |
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參考書目 |
HEINZ HOPF: DIFFERENTIAL GEOMETRY IN THE LARGE, LECTURE NOTES #1000, SPRINGER.
S. S. CHERN: STUDIES IN GLOBAL GEOMETRY AND ANALYSIS, MATH. ASSOCIATION OF AMERICA.
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評量方式
(僅供參考) |
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