CIS 610, Spring 2023

Additional Useful References:

Manifolds and Differential Geometry:

Differential Geometry. Curves, Surfaces, Manifolds, Wolfgang Kuhnel, AMS, SML, Vol. 16, 2002.

An Introduction to Manifolds, Loring Tu, Springer Verlag, Universitext, 2008.

Introduction to Smooth Manifolds, John Lee, Springer Verlag, GTM No. 218, 2006.

Riemannian Geometry, Do Carmo, Manfredo, Birkhauser, 1992.

Differential Geometry of Curves and Surfaces, Do Carmo, Manfredo P., Prentice Hall, 1976.

Geometry of Differential Forms, Shigeyuki Morita, AMS, Translations of Mathematical Monographs, Vol. 201, First Edition.

Riemannian Geometry, Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine, Springer Verlag, Universitext, 2004, Third Edition.

Foundations of Mechanics, R. Abraham, and J. Marsden, Addison Wesley, 1978.

Semi-Riemannian Geometry With Applications to Relativity, Barrett O'Neill, Academic Press, 1983, First Edition.

A Panoramic View of Riemannian Geometry, Marcel Berger, Springer, 2003, First Edition.

Geometry VI. Riemannian Geomety, M.M. Postnikov, Springer, Encyclopaedia of Mathematical Sciences, Vol. 91, 2001, First Edition.

Riemannian Geometry, Takashi Sakai, AMS, Translations of Mathematical Monographs, Vol. 149, 1997, First Edition.

Morse Theory, John Milnor, Princeton University Press, Annals of Mathematics Studies, No. 51, 1969, Third Printing.

Riemannian Geometry. A beginner's guide, Frank Morgan, A.K. Peters, 1998, Second Edition.

Lie Groups:

Lie groups, Lie algebras, and representations, Hall, Brian, Springer (GTM No. 222)

Lie Groups. An introduction through linear Linear groups, Wulf Rossmann, Oxford Science Publications, 2002

An Introduction to Lie Groups and the Geometry of Homogeneous Spaces, Arvanitoyeogos, Andreas, AMS, SML, Vol. 22, 2003

Lectures on Lie Groups and Lie Algebras, Carter, Roger and Segal, Graeme and Macdonald, Ian, Cambridge University Press, 1995

Lie Groups, Duistermaat, J.J. and Kolk, J.A.C., Springer Verlag, Universitext, 2000

Lie Groups Beyond an Introduction, Knapp, Anthony W., Birkhauser, Progress in Mathematics, Vol. 140, Second Edition, 2002

Theory of Lie Groups I, Chevalley, Claude, Princeton University Press, first edition, Eighth printing, Princeton Mathematical Series, No. 8, 1946

Foundations of Differentiable Manifolds and Lie Groups, Warner, Frank, Springer Verlag, GTM No. 94, 1983

Introduction to Lie Groups and Lie Algebras, Sagle, Arthur A. and Walde, Ralph E., Academic Press, 1973

Representation of Compact Lie Groups, Brocker, T. and tom Dieck, T., Springer Verlag, GTM, Vol. 98, 1985

Elements of Mathematics. Lie Groups and Lie Algebras, Chapters 1--3, Bourbaki, Nicolas, Springer, 1989

Introduction a la Theorie des Groupes de Lie Classiques, Mneimne', R. and Testard, F., Hermann, 1997

Some Historical and Leading Figures

David Hilbert,

The MacTutor History of Mathematics archive

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Papers Relevant to the Course Material

  • Morse Theory (11 pages from Milnor's book)   (pdf)
  • On the Early History of the Singular Value Decomposition, by G.W. Stewart   (pdf)
  • Lie Groups, Representation Theory and Symmetric Spaces
    by Wolfgang Ziller (Penn Math Dept.) (pdf)
  • The Geometry of Algorithms with Orthogonality Constraints,
    by Edelman, Aris, and Smith (1998) (pdf)
  • Exponential barycenters, invariant means
    by Xavier Pennec and Vincent Arsigny (2012?) (pdf)
  • Riemannian geometry of Grassmann manifolds with a view on algorithm computation
    by Absil Mahony and Sepulchre (2003) (pdf)
  • Fitting Smooth Paths on Riemannian manifolds
    by Luis Machado and Silva Leite (pdf)
  • The Karcher mean of points on SO(n)
    by Knut Huper and Jonathan Manton (pdf)
  • Lie Group Actions on Manifolds
    by Jurgen Berndt (2003?) (pdf)
  • The greatest mathematical paper of all times (1989)
    A.J. Coleman (pdf)
  • Optimization methods on Riemannian manifolds ...
    by Wolfgang Ring and Benedikt Wirth (pdf)
  • Choice of Riemannian Metrics for Rigid Body Dynamics
    by Milos Zefran, Vijay Kumar and Chris Croke (pdf)
  • Left-Invariant Diffusions on the space of positions and orientations ...
    by Remco Duits, Vijay Kumar and Erik Franken (pdf)
  • Robust Statistics over Riemannian Manifolds for Computer Vision
    by Raghav Subbarao (2008) (pdf)

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