scholarly journals A PROLONGATION OF THE REAL ALMOST-PRODUCT STRUCTURE OF A DIFFERENTIABLE MANIFOLD

1987 ◽  
Vol 20 (3-4) ◽  
Author(s):  
Demetra Demetropoulou-Psomopoulou
Keyword(s):  
Differentiable Manifold ◽  
Product Structure ◽  
The Real ◽  
Almost Product Structure

scholarly journals On refined generalised quasi-adequate transversals

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 299-313
Author(s):  
Xiangjun Kong ◽  
Pei Wang
Keyword(s):  
Structure Theorem ◽  
Interesting Property ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Property A ◽  
The Real ◽  
Spined Product ◽  
Abundant Semigroups

Some properties and characterizations for abundant semigroups with generalised quasiadequate transversals are explored. In such semigroups, an interesting property [?a,b ? Re1S, VSo(a) ? VSo (b) ? 0 ? VSo (a) = VSo (b)] is investigated and thus the concept of refined generalised quasi-adequate transversals, for short, RGQA transversals is introduced. It is shown that RGQA transversals are the real common generalisations of both orthodox transversals and adequate transversals in the abundant case. Finally, by means of two abundant semigroups R and L, a spined product structure theorem for an abundant semigroup with a quasi-ideal RGQA transversal is established.

Note on Almost Product Manifolds and their Tangent Bundles

1966 ◽  
Vol 9 (05) ◽  
pp. 621-630
Author(s):  
Chorng Shi Houh
Keyword(s):  
Tangent Bundle ◽  
Tangent Vector ◽  
Product Structure ◽  
Dimensional Manifold ◽  
Almost Product Structure ◽  
Local Coordinates ◽  
Natural Frame ◽  
Class C ◽  
Tangent Bundles ◽  
Differentiability Class

Let Mn be an n-dimensional manifold of differentiability class C∞ with an almost product structure . Let have eigenvalue +1 of multiplicity p and eigenvalue -1 of multiplicity q where p+q = n and p≧1, q≧1. Let T(Mn) be the tangent bundle of M. T(Mn) is a 2n dimensional manifold of class C∞. Let xi be the local coordinates of a point P of Mn. The local coordinates of T(Mn) can be expressed by 2n variables (xi, yi) where xi are coordinates of the point P and yi are components of a tangent vector at P with respect to the natural frame constituted by the vectior ∂/∂xi at P.

A non-constant invariant function for certain ergodic flows

2008 ◽  
Vol 28 (3) ◽  
pp. 1031-1035
Author(s):  
SOL SCHWARTZMAN
Keyword(s):  
Vector Space ◽  
Real Line ◽  
Differentiable Manifold ◽  
Invariant Function ◽  
Continuous Functions ◽  
The Real ◽  
Almost All ◽  
Uniformly Continuous

AbstractLet U be the vector space of uniformly continuous real-valued functions on the real line $\mathbb {R}$ and let U0 denote the subspace of U consisting of all bounded uniformly continuous functions. If X is a compact differentiable manifold and we are given a flow on X, then we associate with the flow a function F:X→H1(X,U/U0) that is invariant under the flow. We give examples for which the flow on X is ergodic but there is no λ∈H1(X,U/U0) such that F(p)=λ for almost all points p.

scholarly journals The Geometry of Product Conjugate Connections

2013 ◽  
Vol 59 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Adara M. Blaga ◽  
Mircea Crăşmăreanu
Keyword(s):  
Product Structure ◽  
Tensor Fields ◽  
Almost Product Structure ◽  
Conjugate Connections ◽  
Hermitian Geometry ◽  
The Given

Abstract Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of these tensors. Some examples from the geometry of a pair of complementary distributions are discussed and for this case the above structural and virtual tensors are expressed in terms of O’Neill-Gray tensor fields.

scholarly journals PARALLELISM OF DISTRIBUTIONS AND GEODESICS ON F(±a2; ±b2)-STRUCTURE LAGRANGIAN MANIFOLD

2021 ◽  
pp. 157
Author(s):  
Mohammad Nazrul Islam Khan ◽  
Lovejoy S. Das
Keyword(s):  
Tangent Space ◽  
Tensor Field ◽  
Vertical Structure ◽  
Product Structure ◽  
Lagrangian Manifold ◽  
Almost Product Structure ◽  
Vertical Tangent ◽  
B2 Structure

This paper deals with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying (Fv2-a2)(Fv2+a2)(Fv2 - b2)(Fv2 + b2) = 0. In this paper, the authors have proved that if an almost product structure P on the tangent space of a 2n-dimensional Lagrange manifold E is defined and the F(±a2; ±b2)-structure on the vertical tangent space TV (E) is given, then it is possible to define the similar structure on the horizontal subspace TH(E) and also on T(E). In the next section, we have proved some theorems and have obtained conditions under which the distribution L and M are r-parallel, r¯ anti half parallel when r = r¯ . The last section is devoted to proving theorems on geodesics on the Lagrange manifold

AN ALMOST-PRODUCT STRUCTURE ON THE FOLIATED MANIFOLD R.

2020 ◽  
Vol 9 (12) ◽  
pp. 11019-11041
Author(s):  
S. Herinantenaina ◽  
H. S. G. Ravelonirina
Keyword(s):  
Product Structure ◽  
Foliated Manifold ◽  
Almost Product Structure
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