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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...

New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space

Cícero P. Aquino, Henrique F. de Lima (2015)

Archivum Mathematicum

In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space ℍ n + 1 , that is, complete hypersurfaces of ℍ n + 1 whose mean curvature H and normalized scalar curvature R satisfy R = a H + b for some a , b ∈ ℝ . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of ℍ n + 1 . Furthermore, a rigidity result...

Newton transformations on null hypersurfaces

Cyriaque Atindogbé and Hans Tetsing Fotsing (2015)

Communications in Mathematics

Any rigged null hypersurface is provided with two shape operators: with respect to the rigging and the rigged vector fields respectively. The present paper deals with the Newton transformations built on both of them and establishes related curvature properties. The laters are used to derive necessary and sufficient conditions for higher-order umbilicity and maximality we introduced in passing, and develop general Minkowski-type formulas for the null hypersurface, supported by some physical models...

Non-associative geometry and discrete structure of spacetime

Alexander I. Nesterov, Lev Vasilʹevich Sabinin (2000)

Commentationes Mathematicae Universitatis Carolinae

A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.

Non-degenerate hypersurfaces of a semi-Riemannian manifold with a semi-symmetric metric connection

Ahmet Yücesan, Nihat Ayyildiz (2008)

Archivum Mathematicum

We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riemannian manifold and of its a non-degenerate hypersurface with respect to a semi-symmetric metric connection....

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