On Ruled Surfaces in Three-dimensional Minkowski Space PDF Download
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Author: Emad Shonoda
Publisher: LAP Lambert Academic Publishing
ISBN: 9783847322788
Category :
Languages : en
Pages : 100
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Book Description
In a Minkowski three dimensional space we define a semi-inner-product based on the so-called cosine-Minkowski function. We also construct an orthogonal 3D frame in Birkhoff sense, which is canonically adapted to ruled surfaces: beginning with the generator direction we complete this frame using the strictly convex and centrally symmetric unit ball B, which is described either by supporting function or vector representation. Based on the left-orthogonality defined by ball B, the striction curve of a ruled surface in a Minkowski 3-space can be declared in analogy to the Euclidean case. We define the new vector called "Deformation vector" which helps us to find the Frenet-Serret formulae of the ruled surface in the Minkowski three dimension spaces. In these formulae we insert the M-curvatures and M-Torsions with respect to the Minkowski frame. We also can define a covariant differentiation in a Minkowski 3-space, with this can declare geometric M-parallelity of the vector field of the generator of a skew ruled surface along its Minkowski striction curve. Using the second fundamental form the relation between Euclidean and Minkowski normal vectors is given.
Author: Emad Shonoda
Publisher: LAP Lambert Academic Publishing
ISBN: 9783847322788
Category :
Languages : en
Pages : 100
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Book Description
In a Minkowski three dimensional space we define a semi-inner-product based on the so-called cosine-Minkowski function. We also construct an orthogonal 3D frame in Birkhoff sense, which is canonically adapted to ruled surfaces: beginning with the generator direction we complete this frame using the strictly convex and centrally symmetric unit ball B, which is described either by supporting function or vector representation. Based on the left-orthogonality defined by ball B, the striction curve of a ruled surface in a Minkowski 3-space can be declared in analogy to the Euclidean case. We define the new vector called "Deformation vector" which helps us to find the Frenet-Serret formulae of the ruled surface in the Minkowski three dimension spaces. In these formulae we insert the M-curvatures and M-Torsions with respect to the Minkowski frame. We also can define a covariant differentiation in a Minkowski 3-space, with this can declare geometric M-parallelity of the vector field of the generator of a skew ruled surface along its Minkowski striction curve. Using the second fundamental form the relation between Euclidean and Minkowski normal vectors is given.
Author: W. L. Edge
Publisher: Cambridge University Press
ISBN: 1107689678
Category : Mathematics
Languages : en
Pages : 337
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Book Description
This 1931 book contains tables of quintic and sextic ruled surfaces, classified by their double curves and bitangent developables.
Author: Linfan Mao
Publisher: Infinite Study
ISBN: 1599732939
Category :
Languages : en
Pages : 129
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Book Description
Papers on Ruled Surfaces in Minkowski 3-Space, Enumeration of k-Fibonacci Paths Using Infinite Weighted Automata, The Natural Lift Curves and Geodesic Curvatures of the Spherical Indicatrices of The Spacelike-Timelike Bertrand Curve Pair, Magic Properties of Special Class of Trees, and other topics. Contributors: V. Ramachandran, C. Sekar, Rodrigo De Castro, Jose L. Ramirez, Nagesh.H.M, R. Chandrasekhar, A. Vijayalekshmi, S. Suganthi, V. Swaminathan, Arunesh Pandey, V.K. Chaubey, T.N. Pandey, and others.
Author: Linfan Mao
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 129
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Book Description
The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
Author: Stuti Tamta
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 19
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Book Description
In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a place curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples.
Author: Ignace Van De Woestyne
Publisher: World Scientific
ISBN: 9814547514
Category :
Languages : en
Pages : 426
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Book Description
This proceedings consists of papers presented at the international meeting of Differential Geometry and Computer Vision held in Norway and of international meetings on Pure and Applied Differential Geometry held in Belgium. This volume is dedicated to Prof Dr Tom Willmore for his contribution to the development of the domain of differential geometry. Furthermore, it contains a survey on recent developments on affine differential geometry, including a list of publications and a problem list.
Author: Emad Solouma
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 14
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Book Description
In this paper, some geometric properties of equiform Smarandache ruled surfaces in Minkowski space E13 using an equiform frame are investigated. Also, we give the sufficient conditions that make these surfaces are equiform developable and equiform minimal related to the equiform curvatures and when the equiform base curve contained in a plane or general helix. Finally, we provide an example, such as these surfaces.
Author: Leopold Verstraelen
Publisher: World Scientific
ISBN: 9814494704
Category : Mathematics
Languages : en
Pages : 247
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Book Description
Contents:Affine Bibliography 1998 (T Binder et al.)Contact Metric R-Harmonic Manifolds (K Arslan & C Murathan)Local Classification of Centroaffine Tchebychev Surfaces with Constant Curvature Metric (T Binder)Hypersurfaces in Space Forms with Some Constant Curvature Functions (F Brito et al.)Some Relations Between a Submanifold and Its Focal Set (S Carter & A West)On Manifolds of Pseudosymmetric Type (F Defever et al.)Hypersurfaces with Pseudosymmetric Weyl Tensor in Conformally Flat Manifolds (R Deszcz et al.)Least-Squares Geometrical Fitting and Minimising Functions on Submanifolds (F Dillen et al.)Cubic Forms Generated by Functions on Projectively Flat Spaces (J Leder)Distinguished Submanifolds of a Sasakian Manifold (I Mihai)On the Curvature of Left Invariant Locally Conformally Para-Kählerian Metrics (Z Olszak)Remarks on Affine Variations on the Ellipsoid (M Wiehe)Dirac's Equation, Schrödinger's Equation and the Geometry of Surfaces (T J Willmore)and other papers Readership: Researchers doing differential geometry and topology. Keywords:Proceedings;Geometry;Topology;Valenciennes (France);Lyon (France);Leuven (Belgium);Dedication
Author: H. S. Abdel-Aziz
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space.
Author: Andreas Arvanitoyeorgos
Publisher: MDPI
ISBN: 3039280007
Category : Mathematics
Languages : en
Pages : 128
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Book Description
The present Special Issue of Symmetry is devoted to two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces. Submanifold theory originated from the classical geometry of curves and surfaces. Homogeneous spaces are manifolds that admit a transitive Lie group action, historically related to F. Klein's Erlangen Program and S. Lie's idea to use continuous symmetries in studying differential equations. In this Special Issue, we provide a collection of papers that not only reflect some of the latest advancements in both areas, but also highlight relations between them and the use of common techniques. Applications to other areas of mathematics are also considered.
