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Naturally reductive homogeneous ( α , β ) -metric spaces

M. Parhizkar, H.R. Salimi Moghaddam (2021)

Archivum Mathematicum

In the present paper we study naturally reductive homogeneous ( α , β ) -metric spaces. We show that for homogeneous ( α , β ) -metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous ( α , β ) -metric spaces.

Nature of the central singularity in Szekeres models

Pankaj Joshi, Andrzej Królak (1997)

Banach Center Publications

The occurrence and nature of the central naked singularity in aspherical Szekeres models is investigated here, and the strength of the singularity is discussed. The implications for the cosmic censorship hypothesis are considered.

Nearly Kähler and nearly parallel G 2 -structures on spheres

Thomas Friedrich (2006)

Archivum Mathematicum

In some other context, the question was raised how many nearly Kähler structures exist on the sphere 𝕊 6 equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue λ = 12 of the Laplacian acting on 2 -forms. A similar result concerning nearly parallel G 2 -structures on the round sphere 𝕊 7 holds, too. An alternative proof by Riemannian Killing spinors is also indicated.

Neifeld’s Connection Inducedon the Grassmann Manifold

Olga Belova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The work concerns to investigations in the field of differential geometry. It is realized by a method of continuations and scopes of G. F. Laptev which generalizes a moving frame method and Cartan’s exterior forms method and depends on calculation of exterior differential forms. The Grassmann manifold (space of all m -planes) is considered in the n -dimensional projective space P n . Principal fiber bundle of tangent linear frames is arised above this manifold. Typical fiber of the principal fiber bundle...

Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions

Khadiga Arwini, Christopher Dodson (2007)

Open Mathematics

We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the...

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