Differential Geometry 1 (3341.605)
Prerequisite: Differentiable Manifolds
Spring, 2020
I will focus on the "Theory of Connections and Characteristic Classes."
More References
- S.-s. Chern, Vector bundles with a connection in Global Differential Geometry, Studies in Mathematics, Vol. 27, Math. Assoc. Amer. 1987.
- D. Husemoller, Fiber bundles, (First ed., 1966) Third ed., 1994.
- W. Kühnel, Differential Geometry:
Curves–Surfaces–Manifolds, Third Edition, Amer. Math. Soc., 2015.
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I. Madsen and J. Tornehave, From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes,
Cambridge Univ. Press, 1997, 1999.
- L. Tu, Differential Geometry:
Connections, Curvature, and Characteristic Classes, Springer, 2017.
Spring, 2017
Main Topics:
Riemannian Geometry,
Spaces of Constant curvature,
Symmetric Spaces, Hodge Theory, Spectrum.
References:
- M. Berger,
A Panoramic View of Riemannian Geometry, Springer-Verlag, 2003.
- W. Boothby, An Introduction to Differentiable Manifolds and Riemannian
Geometry, Academic Press, 1975.
- M. do Carmo, Riemannian Geometry, Birkhäuser, 1979, 1993.
- S. Gallot, D. Hullin, J. Lafontaine, Riemannian Geometry, Springer, 1993.
- S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978.
-
S. Kobayashi and K. Nomizu,
Foundations of Differential Geometry, Vol I, Vol. II,
Interscience Publishers, 1963, 1969.
- J. M. Lee, Manifolds and Differential Geometry, Amer. Math. Soc., 2009.
- J. Morgan, G. Tian, Ricci Flow and the Poincare Conjecture, Amer. Math. Soc. & Clay Math. Inst., 2007.
- W. Poor, Differential Geometric Structures,
McGraw-Hill, Inc., 1981.
- M. Spivak,
A Comprehensive Introduction to DIFFERENTIAL GEOMETRY,
Vol. I-V (Second ed.), Publish or Perish, Inc., Berkeley, 1979.
- C. Taubes, Differential Geometry, Oxford, 2011.
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W. Thurston, Three-Dimensional Geometry and Topology, Princeton Univ. Press, 1997.
- F. Warner, Foundations of Differentiable Manifolds and Lie Groups,
Scott, Foresmann and Company, 1971.
- J. Wolf, Spaces of constant curvature, 6th ed. 2010.