IMM Pakistan Student 2021 - 2022
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IMM Algeria / 2025 - 2026
Geometry (M1)
TEACHING TEAM
Content
Course description
This course will cover the fundamentals of Differential Geometry, in particular it will introduce the students to differentiable manifolds and their properties. Topics like the tangent space of a manifold, immersions, submersions, vector fields, integration on Manifolds and some concepts related to Lie Groups.
Depending on the time and level of the student the second part of the course will delve deep into Riemannian geometry, covering topics such as Riemannian metrics, covariant derivatives, curvature tensors, Gauss-Bonnet theorem.
Materials
References
References
The main reference of the course is:
Fernandes, R. L. (2024, September). Lectures on Differential Geometry (420 pp.). World Scientific. https://doi.org/10.1142/12733
Some other books covering Differential Geometry, Complex Geometry and Riemannian Geometry are:
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Lee, J. M. (2013). Introduction to smooth manifolds (2nd ed.). Springer. sites.math.washington.edu
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Lee, J. M. (2018). Introduction to Riemannian manifolds (2nd ed.). Springer.
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do Carmo, M. P. (1992). Riemannian geometry. Birkhäuser. link.springer.com+2iri.upc.edu+2
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do Carmo, M. P. (1976). Differential geometry of curves and surfaces. Prentice‑Hall
These can be used as secondary or supplementary references.
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ADMISSIONS
Applicants Are Divided Into Two Groups: "International Applicants" Who Have Foreign Citizenship And "Pakistani Applicants" Who Either Hold Pakistani Citizenship, Have Dual Citizenship, Or Are Pakistanis Residing Outside The Country.
