Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

Quotes

  • Differential geometry originally sneaked into theoretical physics through Einstein's theory of general relativity.
  • 現代幾何学においても、特性類の重要性は減ずるどころかますます大きくなっている。しかも単なるコホモロジー類としてだけでではなく、それを表わす微分形式自 身の詳細な解析がなされるなど、より深い役割を果たすようになってきている。たとえば、de RhamコホモロジーとRiemann計量の関わりを記述する理論である調和積 分論を、ずっと大きな枠組みのなかで一般化するという、壮大な試みが進行中である。そしてこれらの新しい展開のなかで、微分形式は、たとえてみれば生物にとっ ての水や空気のような役割を果たしているといっても過言ではないだろう。
    • It is not too much to say that, so to speak, differential forms play the role of water and air for life.
    • Morita, Shigeyuki (2001). Geometry of Differential Forms(微分形式の幾何学). 岩波書店 (translation published at American Mathematical Society). ISBN 978-0821810453. 

Mathematics
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Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry • Topology

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Ancient Greek mathematics • Euclid's Elements • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica

Other

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