Browsing by Author "Durmaz, Olgun"
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The derivative and tangent operators of a motion in Lorentzian space
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (World Scientific Publ Co Pte Ltd, 2017)In this paper, by using Lorentzian matrix multiplication, L-Tangent operator is obtained in Lorentzian space. The L-Tangent operators related with planar, spherical and spatial motion are computed via special matrix groups. ... -
Dual uzayın temel yapıları ve diferensiyel geometrisi
Durmaz, Olgun (Kırıkkale Üniversitesi, 2022)Bu tez dört bölümden oluşmaktadır. İlk bölüm giriş kısmına ayrılmıştır. Bu bölümde, çalışmanın konusu ile ilgili literatürde yer alan bilgilere yer verilmiştir. Ayrıca, bu kısımda çalışmanın amacı ve önemi belirtilmiştir. ... -
İndirgenmiş riemann metriği ve riemann manifoldları
Durmaz, Olgun (Kırıkkale Üniversitesi, 2015)Bu çalışma üç bölümden oluşmaktadır. Birinci Bölümde diğer bölümler için gerekli olan temel kavramlara ayrılmıştır. İkinci Bölümde Riemann manifoldları tanıtılmıştır. Bir Riemann manifoldu üzerindeki eğri- nin yay uzunluğu, ... -
New Approaches On Dual Space
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (UNIV NIS, 2020)In this paper, we have explained how to define the basic concepts of differential geometry on Dual space. To support this, dual tangent vectors that have (p) over bar as dual point of application have been defined. Then, ... -
On Constraint Manifolds of Lorentz Sphere
Aktas, Busra; Durmaz, Olgun; Gundogan, Hal't (OVIDIUS UNIV PRESS, 2020)The expression of the structure equation of a mechanism is significant to present the last position of the mechanism. Moreover, in order to attain the constraint manifold of a chain, we need to constitute the structure ... -
On Interpretation of Hyperbolic Angle
Aktas, Busra; Gundogan, Halit; Durmaz, Olgun (KYUNGPOOK NATL UNIV, DEPT MATHEMATICS, 2020)Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] ... -
On Parallelizable Spheres in Semi Euclidean Space
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (SOUTHEAST ASIAN MATHEMATICAL SOC-SEAMS, 2020)In Euclidean space, there exist four theorems which show that S-n sphere is not parallelizable for n not equal 1, 3, 7. While three of them are shown by using Bott theorem, the last one is shown by using Hurwitz-Radon ... -
On The Basic Structures Of Dual Space
Aktas, Busra; Durmaz, Olgun; Gundogan, Halit (UNIV NIS, 2020)Topology studies the properties of spaces that are invariant under any continuous deformation. Topology is needed to examine the properties of the space. Fundamentally, the most basic structure required to do math in the ... -
Rodrigues parameters on dual hyperbolic unit sphere H20
Aktas, Busra; Durmaz, Olgun; Gundogan, Halit (Taylor & Francis Ltd, 2018)Rodrigues parameters depend on the tangent of the half rotation angle in Euclidean space but in Dual space, dual Rodrigues parameters contain both rotation angle and distance corresponding the shortest distance between the ... -
Structure equations and constraint manifolds on Lorentz plane
Durmaz, Olgun; Aktas, Busra; Gundogan, Halit (Wiley, 2019)Calculating the structure equation of a chain is important to represent the position of the end link on the chain. Furthermore, the structure equation helps to determine the constraint manifold of the chain. The constraint ...