scholarly journals Entropy of foliations with leafwise Finsler structure

2016 ◽  
Vol 36 (4) ◽  
pp. 499
Author(s):  
Ilona Michalik ◽  
Szymon Walczak
Keyword(s):  
Finsler Structure

On the connections of sub-Finslerian geometry

2019 ◽  
Vol 16 (supp02) ◽  
pp. 1941006
Author(s):  
Layth M. Alabdulsada ◽  
László Kozma
Keyword(s):  
Legendre Transformation ◽  
Nonlinear Connection ◽  
Finsler Structure ◽  
Tangent Manifold ◽  
Finslerian Manifold

A sub-Finslerian manifold is, roughly speaking, a manifold endowed with a Finsler type metric which is defined on a [Formula: see text]-dimensional smooth distribution only, not on the whole tangent manifold. Our purpose is to construct a generalized nonlinear connection for a sub-Finslerian manifold, called [Formula: see text]-connection by the Legendre transformation which characterizes normal extremals of a sub-Finsler structure as geodesics of this connection. We also wish to investigate some of its properties like normal, adapted, partial and metrical.

scholarly journals Finsler-type estimators for the cancer cell population dynamics

2015 ◽  
Vol 98 (112) ◽  
pp. 53-69
Author(s):  
Vladimir Balan ◽  
Jelena Stojanov
Keyword(s):  
Dynamical System ◽  
Population Growth ◽  
Cancer Cell ◽  
Cell Population ◽  
Biological Models ◽  
Cell Population Dynamics ◽  
Finsler Structure ◽  
Cell Population Growth ◽  
Cancer Cell Population ◽  
The Difference

We introduce a Finslerian model related to the classical Garner dynamical system, which models the cancer cell population growth. The Finsler structure is determined by the energy of the deformation field-the difference of the fields, which describe the reduced and the proper biological models. It is shown that a certain locally-Minkowski anisotropic Randers structure, obtained by means of statistical fitting, is able to provide a Zermelo-type drift of the overall cancer cell population growth, which occurs due to significant changes within the cancerous process. The geometric background, the applicative advantages and perspective openings of the constructed geometric structure are discussed.

scholarly journals Negative Vector Bundles and Complex Finsler Structures

1975 ◽  
Vol 57 ◽  
pp. 153-166 ◽  
Author(s):  
Shoshichi Kobayashi
Keyword(s):  
Complex Manifold ◽  
Tangent Bundle ◽  
Vector Bundles ◽  
Finsler Structure

A complex Finsler structure F on a complex manifold M is a function on the tangent bundle T(M) with the following properties. (We denote a point of T(M) symbolically by (z, ζ), where z represents the base coordinate and ζ the fibre coordinate.)

scholarly journals ON FINSLERIZED ABSOLUTE PARALLELISM SPACES

2013 ◽  
Vol 10 (07) ◽  
pp. 1350029 ◽  
Author(s):  
NABIL L. YOUSSEF ◽  
AMR M. SID-AHMED ◽  
EBTSAM H. TAHA
Keyword(s):  
Geometric Structure ◽  
Vector Fields ◽  
Finsler Geometry ◽  
Absolute Parallelism ◽  
Finsler Structure ◽  
New Space ◽  
Curvature Tensors ◽  
Physical Phenomena

The aim of this paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism (GAP)-space. The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized absolute parallelism (parallelizable) space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two structures and their interrelation is carried out. Five connections are introduced and their torsion and curvature tensors derived. Some special Finslerized parallelizable spaces are singled out. One of the main reasons to introduce this new space is that both absolute parallelism and Finsler geometries have proved effective in the formulation of physical theories, so it is worthy to try to build a more general geometric structure that would share the benefits of both geometries.

scholarly journals The Finsler geometry of groups of isometries of Hilbert Space

1987 ◽  
Vol 42 (2) ◽  
pp. 196-222 ◽  
Author(s):  
C. J. Atkin
Keyword(s):  
Hilbert Space ◽  
Lie Algebra ◽  
Orthogonal Group ◽  
Finsler Geometry ◽  
Operator Norm ◽  
Full Description ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Finsler Structure ◽  
Groups Of Isometries

AbstractThe paper deals with six groups: the unitary, orthogonal, symplectic, Fredholm unitary, special Fredholm orthogonal, and Fredholm symplectic groups of an infinite-dimensional Hilbert space. When each is furnished with the invariant Finsler structure induced by the operator-norm on the Lie algebra, it is shown that, between any two points of the group, there exists a geodesic realising this distance (often, indeed, a unique geodesic), except in the full orthogonal group, in which there are pairs of points that cannot be joined by minimising geodesics, and also pairs that cannot even be joined by minimising paths. A full description is given of each of these possibilities.

scholarly journals Weak Finsler structures and the Funk weak metric

2009 ◽  
Vol 147 (2) ◽  
pp. 419-437 ◽  
Author(s):  
ATHANASE PAPADOPOULOS ◽  
MARC TROYANOV
Keyword(s):  
Convex Domain ◽  
Finsler Structure ◽  
Metric Balls

AbstractWe discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we show that these are given by the so-called Funk weak metric. We conclude the paper with a discussion of geodesics, of metric balls, of convexity, and of rigidity properties of the Funk weak metric.

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