Skip to main content
  • Skip to main content
  • Site Map
  • Log in
  • T
  • T
-A A +A
Home
School of Mathematical Sciences
राष्ट्रीय विज्ञान शिक्षा एवंअनुसंधान संस्थान
National Institute of Science Education and Research

NISER

  • Home
    • About SMS
  • People
    • Faculty
    • Staff
    • Students
      • Int. M.Sc.
      • Int.MSc-PhD
      • Ph.D.
    • Postdoc
    • Visitors
    • Alumni
      • Integrated M.Sc
      • PhD
      • Faculty
  • Research
    • Research Areas
    • Publications
  • Curriculum
    • Course Directory
      • UG Core Courses
      • UG Elective Courses
      • PG Core Courses
  • Activity
    • Upcoming
      • Seminar/Colloquium
      • Conference/Sympos/Workshop
      • Meeting
      • Outreach Program
    • Past
      • Seminar/Colloquium
      • Conference/Sympos/Workshop
      • Meeting
      • Outreach
    • MathematiX Club
      • SUMS
  • Blogs
  • Committees
  • Gallery
  • Contact

Breadcrumb

  1. Home
  2. M563 - Differentiable Manifolds and Lie Groups

M563 - Differentiable Manifolds and Lie Groups

By admin_sms on Thu, 17/07/2014 - 14:53
Course No
M563
Credit
4
Approval
2014
UG-Elective
Syllabus
Review of Several variable Calculus: Directional Derivatives, Inverse Function Theorem, Implicit function Theorem, Level sets in R n , Taylor’s theorem, Smooth function with compact support. Manifolds: Differentiable manifold, Partition of Unity, Tangent vectors, Derivative, Lie groups, Immersions and submersions, Submanifolds. Vector Fields: Left invariant vector fields of Lie groups, Lie algebra of a Lie group, Computing the Lie algebra of various classical Lie groups. Flows: Flows of a vector field, Taylor’s formula, Complete vector fields. Exponential Map: Exponential map of a Lie group, One parameter subgroups, Frobenius theorem (without proof). Lie Groups and Lie Algebras: Properties of Exponential function, product formula, Cartan’s Theorem, Adjoint representation, Uniqueness of differential structure on Lie groups. Homogeneous Spaces: Various examples and Properties. Coverings: Covering spaces, Simply connected Lie groups, Universal
covering group of a connected Lie group. Finite dimensional representations of Lie groups and Lie algebras.
Reference Books
  1. D. Bump, “Lie Groups”, Graduate Texts in Mathematics 225, Springer, 2013.
  2. S. Helgason, “Differential Geometry, Lie Groups and Symmetric Spaces”, Graduate Studies in Mathematics 34, American Mathematical Society, 2001.
  3. S. Kumaresan, “A Course in Differential Geometry and Lie Groups”, Texts and Readings in Mathematics 22, Hindustan Book agency, 2002.
  4. F. W. Warner, “Foundations of Differentiable Manifolds and Lie Groups”, Graduate Texts in Mathematics 94, Springer-Verlag, 1983.

Useful links

  • DAE
  • DST
  • JSTOR
  • MathSciNet
  • NBHM
  • ProjectEuclid
  • ScienceDirect

Quick links at NISER

  • NISER HOME
  • NISER Mail
  • Library
  • Intranet
  • Phone Book
  • WEB Portal
  • Office orders

Recent blog posts

Noncommutative Geometry and its Applications (NCG@NISER2020)
Purna Chandra Das : A Prosaic Ode to his Exceptional Life
Best paper award at SENSORNETS 2017 for Deepak Kumar Dalai

Contact us

School of Mathematical Sciences

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

© 2023 School of Mathematical Sciences, NISER, All Rights Reserved.