Research References: Geometry

Differential Geometry and Topology (Math Oriented)

  • John M. Lee: Introduction to Smooth Manifolds (2013)
    Springer, ISBN: 978-1-4419-9981-8

  • Loring W. Tu: An Introduction to Manifolds (2011)
    Springer, ISBN: 978-1-4419-7400-6

  • Jeffrey M. Lee: Manifolds and Differential Geometry (2009)
    AMS, ISBN: 978-1-4704-6982-5

  • Shigeyuki Morita: Geometry of Differential Forms (2001)
    American Mathematical Society, ISBN: 978-0-8218-1045-3

  • Manfredo P. do Carmo: Riemannian Geometry (1992)
    Springer, ISBN: 978-0-8176-3490-2

  • Michael Spivak: A Comprehensive Introduction to Differential Geometry (1999)
    Publish or Perish

Differential Geometry and Topology (Physics Oriented)

  • John Baez and Javier P. Muniain: Gauge Fields, Knots and Gravity (1994)
    World Scientific, ISBN: 978-981-02-1729-7

  • R. W. R. Darling: Differential Forms and Connections (1994)
    Cambridge University Press, ISBN: 978-0521468008

  • Theodore Frankel: The Geometry of Physics (2011)
    Cambridge University Press, ISBN: 978-1107602601

  • William L. Burke: Applied Differential Geometry (1985)
    Cambridge University Press, ISBN: 978-0521269292

  • Bernard F. Schutz: Geometrical Methods of Mathematical Physics (1980)
    Cambridge University Press, ISBN: 978-0521298872

Calculus of Variations

  • Bruce van Brunt: Calculus of Variations (2004)
    Springer, ISBN: 978-1441923165, Springer Link

  • Cornelius Lanczos: The Variational Principles of Mechanics (1986)
    Dover Publications, ISBN: 978-0486650678

  • M. Gelfand and S. V. Fomin: Calculus of Variations (2000)
    Dover Publications, ISBN: 978-0486414485

Classical Mechanics

  • Eugene J. Saletan and Alan H. Cromer: Theoretical Mechanics (1971)
    Wiley, ISBN: 978-0471749868

  • Vladimir I. Arnol’d: Mathematical Methods of Classical Mechanics (1989)
    Springer, ISBN: 978-0-387-96890-2

  • Scheck: Theoretische Physik 1 - Mechanik (2007)
    Springer Lehrbuch, ISBN: 978-3-540-71377-7, Springer Link

  • Andreas Knauf: Mathematische Physik - Klassische Mechanik (2012)
    Springer, ISBN: 978-3-642-20977-2, Springer Link

Geometric Mechanics

  • Jorge V. José and Eugene J. Saletan: Classical Dynamics: A Contemporary Approach (1998)
    Cambridge University Press, ISBN: 978-0521636360

  • Darryl D. Holm: Geometric Mechanics 1 - Dynamics and Symmetry (2011)
    Lecture Notes

  • Darryl D. Holm: Geometric Mechanics 2 - Rotating, Translating and Rolling (2011)
    Lecture Notes

  • Darryl D. Holm, Tanya Schmah, and Cristina Stoica: Geometric Mechanics and Symmetry (2009)
    Oxford University Press, ISBN: 978-0199212903

  • Marsden, Ratiu: Introduction to Mechanics and Symmetry (1999)
    Springer, ISBN: 978-0-387-98643-2

Classical Field Theory

  • Scheck: Theoretische Physik 3 - Klassische Feldtheorie (2010)
    Springer Lehrbuch, ISBN: 978-3-642-03961-4, Springer Link

  • Boris Kosyakov: Introduction to the Classical Theory of Particles and Fields (2007)
    Springer, ISBN: 978-3-642-07422-6, Springer Link

  • Stephen Parrott: Relativistic Electrodynamics and Differential Geometry (1987)
    Springer, ISBN: 978-1-4612-9113-8, Springer Link

Multisymplectic Field Theory

  • Aldaya and J. A. de Azcárraga: Geometric Formulation of Classical Mechanics and Field Theory (1980)
    La Rivista del Nuovo Cimento, Vol. 3, p. 1-66, doi: 10.1007/BF02906204

  • Mark J. Gotay and Jerrold E. Marsden: Momentum Maps and Classical Fields Part I: Covariant Field Theory (1997)
    GiMmsy I, arXiv:physics/9801019

  • Jerrold E. Marsden and Steve Shkoller: Multisymplectic Geometry, Covariant Hamiltonians, and Water Waves (1999)
    Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 125, p. 553-575, arXiv:math/9807086

  • Jerrold E. Marsden, Richard Montgomery, Philip J. Morrison and W. B. Thompson: Covariant Poisson Brackets for Classical Fields (1986)
    Annals of Physics, Vol. 169, p. 29-47

  • Michael Forger and Sandro Vieira Romero: Covariant Poisson Brackets in Geometric Field Theory (2005)
    Communications in Mathematical Physics, Vol. 256, p. 375-410, doi: 10.1007/s00220-005-1287-8, arXiv:math-ph/0408008

  • Arturo Echeverría-Enríquez, Miguel C. Muñoz-Lecanda and Narciso Román-Roy: Geometry of Lagrangian First-order Classical Field Theories (1996)
    Fortschritte der Physik, Vol. 44, p. 235-280, doi: 10.1002/prop.2190440304, arXiv:dg-ga/9505004

  • Arturo Echeverría-Enríquez, Miguel C. Muñoz-Lecanda and Narciso Román-Roy: Geometry of Multisymplectic Hamiltonian First-order Field Theories (2000)
    Journal of Mathemathical Physics, Vol. 41, p. 7402, doi:10.1063/1.1308075, arXiv:math-ph/0004005