Lexic.us

Definition of Riemannian geometry

1. Noun. (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle. "Bernhard Riemann pioneered elliptic geometry"

Definition of Riemannian geometry

1. Noun. the branch of differential geometry that studies Riemannian manifolds ¹

¹ Source: wiktionary.com

Lexicographical Neighbors of Riemannian Geometry

Literary usage of Riemannian geometry

Below you will find example usage of this term as found in modern and/or classical literature:

1. Geometry of Riemannian Spaces by Elie Cartan (1983)
"(11) We shall apply this last method to the study of problems is Riemannian geometry. II. EXTENSIONS TO THE THEORY OF SURFACES EMBEDDED IN A ..."

2. Geometric Structures in Nonlinear Physics by Robert Hermann (1991)
"Riemannian geometry AND THE IDEAL FLUID VARIATIONAL PRINCIPLE It has long been recognized (eg in ... In this Section, we will add Riemannian geometry. 1. ..."

3. Topics in the Mathematics of Quantum Mechanics by Robert Hermann (1973)
"Riemannian geometry OF THE KINEMATIC SPACES Let us suppose that G as defined in ... For the concepts of manifold theory and Riemannian geometry used here, ..."

4. Energy Momentum Tensors by Robert Hermann (1976)
"Riemannian geometry Let 14 be a manifold. A Riemannian metric on M is defined by an F(M)-bilinear mapping 8:V(M)xV(M)—9F(M) such that: 8(X,Y) — 8(Y,X) for X ..."

5. The Encyclopedia Americana: A Universal Reference Library Comprising the ...by Scientific American, inc by Scientific American, inc (1905)
"... and to-day pure two-dimensional spherics is not only the best Euclidean analogue of a Riemannian geometry, but inversely the geometry of two- ..."

6. Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field by George Abram Miller, Frederick Shenstone Woods, Leonard Eugene Dickson, Thomas Franklin Holgate, Edward Vermilye Huntington, David Eugene Smith, Oswald Veblen, Gilbert Ames Bliss, J. W. A. (Jacob William Albert) Young (1911)
"In the Riemannian geometry the lines AC and LK eventually intersect. Hence, if AC is sufficiently long CK< AL, and therefore CK is always less than AL and ..."

7. Science by American Association for the Advancement of Science (1883)
"It employs a tensor field and a Riemannian geometry. ... This theory also uses Riemannian geometry and a tensor field, but it employs an additional scalar ..."

8. Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field by Jacob William Albert Young, Oswald Veblen, Thomas Franklin Holgate, Frederick Shenstone Woods, Edward Vermilye Huntington, George Abram Miller, Gilbert Ames Bliss, Leonard Eugene Dickson, David Eugene Smith (1911)
"In the Riemannian geometry the lines AC and LK eventual!y intersect. Hence, if AC is sufficiently long CK< AL, and therefore CK is always less than AL and ..."

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