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1

Sphere – to – spheroid comparison – numerical analysis

Lenart A. S.

Polish Maritime Research

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2017

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nr 4

4--9

EN

Differences of orthodromic distances calculated on the sphere in comparison to the spheroid are numerically analyzed in the full range of departure point latitudes, courses over the ground and orthodromic distances for the global and limited range of latitudes. Optimum solutions for the radii of the sphere are provided.

2

Module of a geodesic foliation on the flat torus

Kaźmierczak A.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 4

61--72

EN

We study properties of geodesic foliations on the flat, n-dimensional torus. Using the isomorphism of the Hodge star, we obtain some facts concerning compact totally geodesic surfaces (which are the leaves of geodesic foliations). We compute the p-module of a geodesic foliation. On the basis of these results, we derive a kind of reciprocity formula for the product of modules of two orthogonal foliations. We relate this product with the number of intersections of their leaves. We also obtain a formula for a product of modules of a finite number of geodesic foliations.

3

A useful characterization of some real hypersurfaces in a nonflat complex space form

Itoh T., Maeda S.

Bulletin of the Polish Academy of Sciences. Mathematics

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2006

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Vol. 54, no 2

125-136

EN

We characterize totally η-umbilic real hypersurfaces in a nonflat complex space form [...](c) (= CPn(c) or CHn(c)) and a real hypersurface of type (A2) of radius π/(2√c) in CPn(c) by observing the shape of some geodesies on those real hypersurfaces as curves in the ambient manifolds (Theorems 1 and 2).

4

Geodesics in the sub-Lorentzian geometry

Grochowski M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2002

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Vol. 50, no 2

161-178

EN

The aim of this paper is to introduce the notion of sub-Lorentzian manifolds (which is done by analogy to sub-Riemannian manifolds) and to describe basic properties of such manifolds. In particular, we investigate problems related to the existence of the longest curves between two given points, and examine some conditions for continuity and differentiability of the (local) sub-Lorentzian distance function.

5

Differential properties of the sub-Riemannian distance function

Grochowski M.

Bulletin of the Polish Academy of Sciences. Mathematics

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2002

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Vol. 50, no 1

93-101

EN

Let (M, H, g) be a sub-Riemannian manifold. Fix a point [p_0 belongs to M] and denote by f the sub-Riemannian distance from [p_0]. It is proved that f is smooth on an open and dense subset of a certain neighbourhood of a regular geodesic. On the other hand, each minimizing geodesic around which f is smooth is regular.