### Differential geometry

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. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. Since the late 19th century, differential geometry has grown into a field concerned more generally with the geomet...

### Diffeomorphism

In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are smooth. Given two manifolds M {\displaystyle M} and N {\displaystyle N} , a differentiable map f : M → N {\displaystyle f\colon M\rightarrow N}...

### Information geometry

Information geometry is an interdisciplinary field that applies the techniques of differential geometry to study probability theory and statistics. It studies statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions. Historically, information geometry can be traced back to the work of C. R. Rao, who was the first to treat the Fisher matrix as a Riemannian metric. The modern theory is largely due to Shun'ichi Amari, whose work has been greatly inf...

### Differential Geometry (Dover Books on Mathematics)

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### Differential Geometric Structures (Dover Books on Mathematics)

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### Elementary Differential Geometry, Revised 2nd Edition

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### An Introduction to Differential Geometry (Dover Books on Mathematics)

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### Schaum's Outline of Differential Geometry (Schaum's)

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### Applicable Differential Geometry (London Mathematical Society Lecture Note Series)

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### A First Course in Differential Geometry (Surfaces in Euclidean Space)

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