Results 231 to 240 of about 99,297 (282)

Spatial correlation at the boson peak frequency in amorphous materials. [PDF]

open access: yesNat Commun
Li XY   +7 more
europepmc   +1 more source

Affine Connection Complexes

Acta Applicandae Mathematica, 1999
The author abstracts the properties of exterior forms \(\{\bigwedge^\star {\mathcal E}, d\}\) where \({\mathcal E}^\star\) is the tensor algebra generated by the dual \(C^\infty (M)\)-module \({\mathcal E}\) of 1-forms on a differentiable manifold \(M\), to obtain geometric properties. In his words: ``An affine connection is traditionally regarded as a
openaire   +2 more sources

On affine maps between affinely connected manifolds

Geometriae Dedicata, 1990
Every affine map between two affinely connected manifolds is the composition of an affine submersion and an affine immersion; and the inverse image of an autoparallel submanifold by such maps is the union of autoparallel submanifolds. Furthermore, the Lie group of all affine transformations of an affinely connected manifold carries the compact-open ...
Martin Linden, Helmut Reckziegel
openaire   +1 more source

Almost Geodesics and Special Affine Connection

Results in Mathematics, 2020
An almost geodesic of an affine connection \(\nabla\) on a manifold is a curve \(x(t)\) so that \[ \nabla^2_{\dot{x}}\dot{x}=a\nabla_{\dot{x}} \dot{x}+b\dot{x}, \] for some real-valued continuous functions \(a(t),b(t)\). The authors consider a curve in the Euclidean space and a translation invariant affine connection on the Euclidean space.
Olga Belova, Josef Mikeš
openaire   +2 more sources

The affine connection

2021
Abstract The connection and the covariant derivative are treated. Connection coefficients are introduced in their role of expressing the change in the coordinate basis vectors between neighbouring points. The covariant derivative of a vector is then defined.
openaire   +1 more source

Codazzi-Equivalent Affine Connections

Results in Mathematics, 2009
We extend the concept of Codazzi-equivalence from Riemannian metrics in [14] to affine connections. Applications to relative hypersurface theory show that this concept simplifies the investigation of pairs of hypersurfaces with parallel normalization, moreover we get a better understanding of the affine Gaus maps. We give a new proof of Calabi’s global
Angela Schwenk-Schellschmidt, Udo Simon
openaire   +1 more source

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