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Definition of Riemannian
1. Adjective. Of or relating to Riemann's non-Euclidean geometry.
Definition of Riemannian
1. Adjective. (mathematics) Relating to the branch of geometry inspired by (w Bernhard Riemann). ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Riemannian
Literary usage of Riemannian
Below you will find example usage of this term as found in modern and/or classical literature:
1. Yang-Mills, Kaluza-Klein, and the Einstein Program by Robert Hermann (1978)
"(Just as the curvature of a Riemannian metric associated with a gravitational
field provides the field equation, i . e., the Einstein equations. ..."
2. Development of Mathematics in the 19th Century by Felix Klein, Robert Hermann (1979)
"SUBMANIFOLDS OF THE SPACE OF GEODESICS OF A Riemannian MANIFOLD Let Z be a manifold
with a Riemannian metric 'W ~* <V1'V2> ' Let S(Z) be the unit tangent ..."
3. Topics in the Mathematics of Quantum Mechanics by Robert Hermann (1973)
"Above all, each of the "kinematic" spaces described in Section 3 inherits a
Riemannian metric, since it may be imbedded h as a subspace of a Cartesian ..."
4. Cartanian Geometry, Nonlinear Waves, and Control Theory. by Robert Hermann (1980)
"A possible clue to such a study is to be found in work by Elie Cartan (13] on
what are called “isoparametric functions” on the Riemannian manifold. ..."
5. Ricci and Levi-Civita's Tensor Analysis Paper by Robert Hermann (1975)
"It is easy to see that the natural projection map M ->• a\n has (in the regular
case) this Riemannian submersion property. ..."
6. Topics in Physical Geometry by Robert Hermann (1988)
"However, they appear in a form that is dual to the “Riemannian ... A co-Riemannian
metric on X is a cross-section gd of the symetric tensor product bundle ..."
7. Geometric Structures in Nonlinear Physics by Robert Hermann (1991)
"CO-Riemannian METRICS The geometric objects that are dual to the ... A Co-Riemannian
metric on X is the geometric structure defined by a map: such that: pd ..."
8. Topics in the Geometric Theory of Integrable Mechanical Systems by Robert Hermann (1984)
"Let < , > denote the inner product that the Riemannian metric defines on differential
forms. (Thus, < , > is really the dual co-Riemannian metric. ..."
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