課程資訊

Differential Geometry (Ⅰ)

102-1

MATH7301

221 U2930

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1021geo

Modern differential geometry encompasses a wide array of techniques and results. Beginning with an overview of smooth differential manifolds (including coordinates, vector ﬁelds, tangent bundles, differential forms, tensors) we will then discuss Riemannian manifolds (those for which metric notions such as length, volume, etc. are deﬁned), connections (leading to Hessian and Laplacian), exponential map, geodesics, submanifolds, and curvature.
A significant part of the remainder of the course will study the effects curvature has on geometry and topology. In particular, this includes the linear theory of de Rham theorem and Hodge theory of harmonic forms, Bochner principles, and the non-linear theory on applications of second variational formula for geodesics and minimal sub-manifolds.

Provide an essential foundation in differential geometry for students aiming at using it in various kind of further applications in mathematics or modern sciences, and open a way to pursue work or research in modern geometry.

Undergraduate required courses: Linear algebra, advanced calculus, algebra, geometry, complex analysis, introduction to ODE, introduction to PDE.
Optional (not absolutely required): Topology, algebraic topology.

Office Hours

1. Jurgen, Jost: Riemannian Geometry and Geometric Analysis.
2. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I and II.
3. Schoen and Yau: Lectures on Differential Geometry.
4. Y. Matsushima, Differentiable Manifolds.
5. M. Spivak : A Comprehensive Introduction to Differential Geometry, I-II.

(僅供參考)

 No. 項目 百分比 說明 1. home work 50% 2. Final 50%

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