Results 241 to 250 of about 1,198,709 (262)
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Journal of Mathematical Sciences, 2002
The authors present a survey of Riemannian geometry that sketches the main developments in that subject through about 1985; no bibliographic references after that date exist. They begin with historical remarks and brief descriptions of the contributions of Lobachevski, Gauss, Riemann, F. Klein, E. Cartan, Ricci and Levi-Civita.
Trofimov, V. V., Fomenko, A. T.
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The authors present a survey of Riemannian geometry that sketches the main developments in that subject through about 1985; no bibliographic references after that date exist. They begin with historical remarks and brief descriptions of the contributions of Lobachevski, Gauss, Riemann, F. Klein, E. Cartan, Ricci and Levi-Civita.
Trofimov, V. V., Fomenko, A. T.
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Extended Riemannian Geometry I: Local Double Field Theory
Annales de l'Institute Henri Poincare. Physique theorique, 2016We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds, and it yields extended notions of symmetries, dynamical data and ...
Andreas Deser, Christian Sämann
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Generalizing Riemannian geometry
Journal of Mathematical Physics, 1973The properties of Riemannian geometry necessary to relativity have been used as a basis to derive a more general geometry. Emphasis is placed on a natural development with the result of considerable generalization. Several examples are discussed including the Brans-Dicke field equation which are but one special case of the new manifolds.
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Satellites and Riemannian geometry
Celestial Mechanics, 1969In an axially symmetric three-dimensional Riemann-spacegik(u1,u2)−u3 represents the cyclic parameter-, a gravitational potential ϕ(u1,u2) is given. For all masspoints with equal total energy and equal angular momentum there exists a function Ψ(u1,u2) by means of which the equations of motion can be reduced to a simple ordinary second-order differential
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Embeddings and immersions in Riemannian geometry
Russian Mathematical Surveys, 1970zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M L Gromov, V. A. Rokhlin
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1966
Publisher Summary This chapter focuses on Riemannian geometry. In studying the geometry of a surface in E3, it is found that some of its most important geometric properties belong to the surface itself and not the surrounding Euclidean space. Gaussian curvature is a prime example; although defined in terms of shape operators, it belongs to this ...
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Publisher Summary This chapter focuses on Riemannian geometry. In studying the geometry of a surface in E3, it is found that some of its most important geometric properties belong to the surface itself and not the surrounding Euclidean space. Gaussian curvature is a prime example; although defined in terms of shape operators, it belongs to this ...
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On the Geometry of Almost Golden Riemannian Manifolds
, 2017An almost Golden Riemannian structure $$(\varphi ,g)$$(φ,g) on a manifold is given by a tensor field $$\varphi $$φ of type (1,1) satisfying the Golden section relation $$\varphi ^{2}=\varphi +1$$φ2=φ+1, and a pure Riemannian metric g, i.e., a metric ...
F. Etayo +2 more
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Biharmonic Submanifolds and Biharmonic Maps in Riemannian Geometry
, 2020Bang‐Yen Chen, Ye-lin Ou
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1990
We have already got used to the fact that many quantities are given as numerical functions of a point in space. For example, the distance from a point to a certain fixed centre, etc. If we have several such quantities at our disposal, we already have several functions of a point (or, so to say, the vector function of this point).
S. P. Novikov +1 more
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We have already got used to the fact that many quantities are given as numerical functions of a point in space. For example, the distance from a point to a certain fixed centre, etc. If we have several such quantities at our disposal, we already have several functions of a point (or, so to say, the vector function of this point).
S. P. Novikov +1 more
openaire +2 more sources