Hans Stephani's Relativity is still in print. And there's a good reason.
M. Francaviglia has written: 'Applications of infinite-dimensional differential geometry to general relativity' -- subject(s): Differential Geometry, Function spaces, General relativity (Physics) 'Elements of differential and Riemannian geometry' -- subject(s): Differential Geometry, Riemannian Geometry
T. Sakai has written: 'Riemannian geometry' -- subject(s): Geometry, Riemannian, Riemannian Geometry
Thierry Aubin has written: 'Some nonlinear problems in Riemannian geometry' -- subject(s): Geometry, Riemannian, Nonlinear theories, Riemannian Geometry
Marcel Berger has written: 'A panoramic view of Riemannian geometry' -- subject(s): Riemannian Geometry 'Geometry revealed' -- subject(s): Differential Geometry
Luther Pfahler Eisenhart has written: 'Non-Riemannian Geometry (Colloquium Publications (Amer Mathematical Soc))' 'Non-Riemannian geometry' -- subject(s): Differential Geometry, Geometry, Differential 'Riemannian geometry, by Luther Pfahler Eisenhart' -- subject(s): Differential Geometry, Geometry, Differential, Riemann surfaces 'Transformations of surfaces' -- subject(s): Surfaces, Transformations (Mathematics)
Riemann equations, particularly in the context of Riemann surfaces and Riemannian geometry, are used in various fields such as mathematics, physics, and engineering. They are essential in complex analysis, where they help in understanding multi-valued functions and their properties. In physics, Riemannian geometry plays a crucial role in general relativity, describing the curvature of space-time. Additionally, they find applications in optimization problems and in the study of differential equations.
The German mathematician Georg Friedrich Bernhard Riemann (1826 - 1866).
Roberto Torretti has written: 'The Philosophy of Physics (The Evolution of Modern Philosophy)' 'Relativity and geometry' -- subject(s): Differential Geometry, Geometry, Geometry, Differential, Philosophy, Relativity (Physics)
Clement V. Durell has written: 'Advanced trigonometry' 'A new geometry for schools' 'A course of plane geometry for advanced students' -- subject(s): Geometry, Plane, Plane Geometry 'Readable relativity' -- subject(s): Relativity (Physics)
Four great mathematicians who contributed to geometry are Pythagoras, Euclid, Rene Descartes and Bernhard Riemann. Pythagoras contributed the Pythagorean theorem. Euclid's geometrical works helped develop geometry in many ways. Descartes contributed Cartesian Geometry. Riemann's contribution can be seen in the form of Riemannian Geometry.
Pi is only constant in Euclidean Geometry, it is not the same in other Geometries. In the non-Euclidean geometry that Relativity theory uses the difference between PiE and PiNE is extremely small, approaching zero.
Euclidean geometry has become closely connected with computational geometry, computer graphics, convex geometry, and some area of combinatorics. Topology and geometry The field of topology, which saw massive developement in the 20th century is a technical sense of transformation geometry. Geometry is used on many other fields of science, like Algebraic geometry. Types, methodologies, and terminologies of geometry: Absolute geometry Affine geometry Algebraic geometry Analytic geometry Archimedes' use of infinitesimals Birational geometry Complex geometry Combinatorial geometry Computational geometry Conformal geometry Constructive solid geometry Contact geometry Convex geometry Descriptive geometry Differential geometry Digital geometry Discrete geometry Distance geometry Elliptic geometry Enumerative geometry Epipolar geometry Euclidean geometry Finite geometry Geometry of numbers Hyperbolic geometry Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Numerical geometry Ordered geometry Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian geometry Ruppeiner geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation geometry Tropical geometry