On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3 Space
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On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3 Space
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Author : Emad Solouma
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
On Geometry Of Equiform Smarandache Ruled Surfaces Via Equiform Frame In Minkowski 3 Space written by Emad Solouma and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
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.
Investigation Of Special Type Smarandache Ruled Surfaces Due To Rotation Minimizing Darboux Frame
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Author : Emad Solouma
language : en
Publisher: Infinite Study
Release Date : 2024-01-01
Investigation Of Special Type Smarandache Ruled Surfaces Due To Rotation Minimizing Darboux Frame written by Emad Solouma and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-01 with Mathematics categories.
This study begins with the construction of type-Π Smarandache ruled surfaces, whose base curves are Smarandache curves derived by rotation-minimizing Darboux frame vectors of the curve in E3. The direction vectors of these surfaces are unit vectors that convert Smarandache curves. The Gaussian and mean curvatures of the generated ruled surfaces are then separately calculated, and the surfaces are required to be minimal or developable. We report our main conclusions in terms of the angle between normal vectors and the relationship between normal curvature and geodesic curvature. For every surface, examples are provided, and the graphs of these surfaces are produced.
Pointwise 1 Type Gauss Map Os Developable Smarandache Rules Surfaces
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Author : Stuti Tamta
language : en
Publisher: Infinite Study
Release Date : 2023-01-01
Pointwise 1 Type Gauss Map Os Developable Smarandache Rules Surfaces written by Stuti Tamta and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
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.
Smarandache Ruled Surfaces According To Frenet Serret Frame Of A Regular Curve In E3
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Author : Soukaina Ouarab
language : un
Publisher: Infinite Study
Release Date :
Smarandache Ruled Surfaces According To Frenet Serret Frame Of A Regular Curve In E3 written by Soukaina Ouarab and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper, we introduce original definitions of Smarandache ruled surfaces according to Frenet-Serret frame of a curve in E3. It concerns TN-Smarandache ruled surface, TB-Smarandache ruled surface, and NB-Smarandache ruled surface. We investigate theorems that give necessary and sufficient conditions for those special ruled surfaces to be developable and minimal. Furthermore, we present examples with illustrations.
Differential Geometry
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Author : Wolfgang Kühnel
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Differential Geometry written by Wolfgang Kühnel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.
Structures On Manifolds
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Author : Masahiro Kon
language : en
Publisher: World Scientific
Release Date : 1985-02-01
Structures On Manifolds written by Masahiro Kon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-02-01 with categories.
Contents: Riemannian ManifoldsSubmanifolds of Riemannian ManifoldsComplex ManifoldsSubmanifolds of Kaehlerian ManifoldsContact ManifoldsSubmanifolds of Sasakian Manifoldsf-StructuresProduct ManifoldsSubmersions Readership: Mathematicians. Keywords:Riemannian Manifold;Submanifold;Complex Manifold;Contact Manifold;Kaehlerian Manifold;Sasakian Manifold;Anti-Invariant Submanifold;CR Submanifold;Contact CR Submanifold;Submersion
An Introduction To Clifford Algebras And Spinors
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Author : Jayme Vaz Jr.
language : en
Publisher: Oxford University Press
Release Date : 2016
An Introduction To Clifford Algebras And Spinors written by Jayme Vaz Jr. and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
This book is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
Differential Geometry Of Lightlike Submanifolds
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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-02
Differential Geometry Of Lightlike Submanifolds written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-02 with Mathematics categories.
This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.
Plithogenic Set An Extension Of Crisp Fuzzy Intuitionistic Fuzzy And Neutrosophic Sets Revisited
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Plithogenic Set An Extension Of Crisp Fuzzy Intuitionistic Fuzzy And Neutrosophic Sets Revisited written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values.
On Ruled Surfaces In Three Dimensional Minkowski Space
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Author : Emad Shonoda
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-12
On Ruled Surfaces In Three Dimensional Minkowski Space written by Emad Shonoda and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12 with categories.
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.