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 - Ralph Abraham, Jerrold E. Marsden and Tudor S. Ratiu: Manifolds, Tensor Analysis, and Applications (1988)
Springer, ISBN: 978-1-4612-1029-0 - Shigeyuki Morita: Geometry of Differential Forms (2001)
American Mathematical Society, ISBN: 978-0-8218-1045-3 - William L. Burke: Applied Differential Geometry (1985)
Cambridge University Press, ISBN: 978-0521269292 - Michael Spivak: A Comprehensive Introduction to Differential Geometry (1999)
Publish or Perish - Keith Burns and Marian Gidea: Differential Geometry and Topology (2005)
Chapman & Hall, ISBN: 978-1584882534 - Ruben Aldrovandi and Jose Geraldo Pereira: An Introduction to Geometrical Physics (1995)
World Scientific, ISBN: 978-981-02-2232-1 - Vladimir G. Ivancevic and Tijana T. Ivancevic: Applied Differential Geometry (2007)
World Scientific, ISBN: 978-981-270-614-0
Differential Geometry and Topology (Physics Oriented)
- Gerardo F. Torres del Castillo: Differentiable Manifolds - A Theoretical Physics Approach (2012)
Birkhäuser, ISBN: 978-0-8176-8270-5 - Mikio Nakahara: Geometry, Topology and Physics (2003)
Taylor & Francis, ISBN: 978-0750306065 - Theodore Frankel: The Geometry of Physics (2011)
Cambridge University Press, ISBN: 978-1107602601 - Stephen Lovett: Differential Geometry of Manifolds with Applications to Physics (2010)
Taylor & Francis, ISBN: 978-1568814575 - Marcelo Epstein: The Geometrical Language of Continuum Mechanics (2010)
Cambridge University Press, ISBN: 978-0521198554 - Marián Fecko: Differential Geometry and Lie Groups for Physicists (2006)
Cambridge University Press, ISBN: 978-0521845076 - Michael Stone and Paul Goldbart: Mathematics for Physics - A Guided Tour for Graduate Students (2009)
Cambridge University Press, ISBN: 978-0521854030 - Bernard F. Schutz: Geometrical Methods of Mathematical Physics (1980)
Cambridge University Press, ISBN: 978-0521298872 - Chris J. Isham: Modern Differential Geometry for Physicists (1999)
World Scientific Publishing, ISBN: 978-9810235628 - Helmut Eschrig: Topology and Geometry for Physics (2011)
Springer Lecture Notes in Physics, Vol. 822, ISBN: 978-3-642-14699-2
Classical Mechanics
- Scheck: Theoretische Physik 1 - Mechanik (2007)
Springer Lehrbuch, ISBN: 978-3-540-71377-7, Springer Link - 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 - Vladimir I. Arnol’d: Mathematical Methods of Classical Mechanics (1989)
Springer, ISBN: 978-0-387-96890-2 - Marsden, Ratiu: Introduction to Mechanics and Symmetry (1999)
Springer, ISBN: 978-0-387-98643-2 - Andreas Knauf: Mathematische Physik - Klassische Mechanik (2012)
Springer, ISBN: 978-3-642-20977-2, Springer Link
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 - Noel Doughty: Lagrangian Interaction - An Introduction To Relativistic Symmetry In Electrodynamics And Gravitation (1990)
Addison-Wesley, ISBN: 978-0201416251
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
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