Leseprobe
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Riemannian Geometry
Luther Pfahler Eisenhart
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
In his classic work of geometry, Euclid focused on the properties of flat surfaces. In the age of exploration, mapmakers such as Mercator had to concern themselves with the properties of spherical surfaces. The study of curved surfaces, or non-Euclidean geometry, flowered in the late nineteenth century, as mathematicians such as Riemann increasingly questioned Euclid's parallel postulate, and by relaxing this constraint derived a wealth of new results. These seemingly abstract properties found immediate application in physics upon Einstein's introduction of the general theory of relativity.
In this book, Eisenhart succinctly surveys the key concepts of Riemannian geometry, addressing mathematicians and theoretical physicists alike.
Kundenbewertungen
Outer product, Partial differential equation, Big O notation, Determinant, Differential form, Frenet–Serret formulas, Metric tensor, Unit vector, Quantity, First variation, Parametric equation, Orthogonality, Simultaneous equations, Homogeneous coordinates, Quadratic form, Absolute value, 0O, Symmetric tensor, Second fundamental form, Mixed tensor, Curvature, Euclidean vector, Constant curvature, Euclidean space, Riemannian geometry, Infinitesimal transformation, Homotopy, Constant of integration, Existential quantification, Riemannian manifold, Affine connection, Integral curve, Proportionality (mathematics), Cartesian coordinate system, Linear differential equation, Minkowski space, Zero of a function, Kronecker delta, Special case, Einstein notation, Hypersurface, Covariance and contravariance of vectors, Derivative, Prime number, Maxima and minima, Infinitesimal generator (stochastic processes), Geometry, Three-dimensional space (mathematics), Linear map, Ricci curvature, Vector field, Coefficient, Covariant derivative, Sylvester's law of inertia, Equation, Tensor density, Umbilical point, Null vector, Christoffel symbols, Linear combination, Basis (linear algebra), Conformal map, Scalar curvature, Coordinate system, Hypersphere, Semigroup, Theorem, Summation, Quadric, Parameter