CIS 610, Spring 2023

Additional Useful References:

Manifolds and Differential Geometry:

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. 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

The MacTutor History of Mathematics archive

The Mathematics Genealogy Project

Papers Relevant to the Course Material