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On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group

Author: Zuhal Kucukarslan Yuzbasi

Publisher: Infinite Study

Published: 2022-01-01

Total Pages: 8

ISBN-13:

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This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.

Book Synopsis On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group by : Zuhal Kucukarslan Yuzbasi

Download or read book On Parametric Surfaces with Constant Mean Curvature Along Given Smarandache Curves in Lie Group written by Zuhal Kucukarslan Yuzbasi and published by Infinite Study. This book was released on 2022-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper finds sufficient conditions to determine a surface whose mean curvature along a given Smarandache curve is constant in a three-dimensional Lie group. This is accomplished by using the Frenet frames of the specified curve to express surfaces that span the 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves parametrically. In terms of the curvatures of given Smarandache curves, marching scale functions, and their partial derivatives, the mean curvatures of these surfaces along the given 𝑇𝑁, 𝑁𝐵, and 𝑇𝐵 Smarandache curves are determined. Sufficient conditions are found to maintain the provided mean curvatures of the resulting surfaces at a constant value. Finally, some examples are provided.

Constant Mean Curvature Surfaces in Homogeneous Manifolds

Author: Julia Plehnert

Publisher: Logos Verlag Berlin GmbH

Published: 2012

Total Pages: 94

ISBN-13: 3832532064

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In this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC H surfaces in ∑(k) x R with H ∈ [0,1/2] and k + 4H2 ≤ 0, has genus 0,2 k ends and k-fold dihedral symmetry, k ≥ 2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1/2 surface in H2 ∈ R with k ends, genus 1 and k-fold dihedral symmetry, k ≥ 3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1/2 all surfaces are Alexandrov-embedded.

Book Synopsis Constant Mean Curvature Surfaces in Homogeneous Manifolds by : Julia Plehnert

Download or read book Constant Mean Curvature Surfaces in Homogeneous Manifolds written by Julia Plehnert and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC H surfaces in ∑(k) x R with H ∈ [0,1/2] and k + 4H2 ≤ 0, has genus 0,2 k ends and k-fold dihedral symmetry, k ≥ 2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1/2 surface in H2 ∈ R with k ends, genus 1 and k-fold dihedral symmetry, k ≥ 3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1/2 all surfaces are Alexandrov-embedded.

Special Smarandache Ruled Surfaces According to Flc Frame

Author: Suleyman Senyurt

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 18

ISBN-13:

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In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled surfaces by using Maple17.

Book Synopsis Special Smarandache Ruled Surfaces According to Flc Frame by : Suleyman Senyurt

Download or read book Special Smarandache Ruled Surfaces According to Flc Frame written by Suleyman Senyurt and published by Infinite Study. This book was released on 2023-01-01 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled surfaces by using Maple17.

Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31

Author: Sungwook Lee

Publisher:

Published: 2002

Total Pages: 174

ISBN-13:

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Book Synopsis Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31 by : Sungwook Lee

Download or read book Space-like Surfaces of Constant Mean Curvature in de Sitter 3-space S31 written by Sungwook Lee and published by . This book was released on 2002 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Surfaces of Constant Mean Curvature in Constant Curvature Manifolds

Author: D. Hoffmann

Publisher:

Published: 1971

Total Pages: 56

ISBN-13:

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Book Synopsis Surfaces of Constant Mean Curvature in Constant Curvature Manifolds by : D. Hoffmann

Download or read book Surfaces of Constant Mean Curvature in Constant Curvature Manifolds written by D. Hoffmann and published by . This book was released on 1971 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Groups: The classical differential geometry of curves and surfaces

Author: Sophus Lie

Publisher:

Published: 1975

Total Pages:

ISBN-13:

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Book Synopsis Lie Groups: The classical differential geometry of curves and surfaces by : Sophus Lie

Download or read book Lie Groups: The classical differential geometry of curves and surfaces written by Sophus Lie and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES)

Author: Linfan MAO

Publisher: Infinite Study

Published:

Total Pages: 135

ISBN-13:

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The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, 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, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Book Synopsis MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES) by : Linfan MAO

Download or read book MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES) written by Linfan MAO and published by Infinite Study. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical combinatorics is a subject that applying combinatorial notion to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr.Linfan MAO on mathematical sciences. TheMathematical Combinatorics (International Book Series) is a fully refereed international book series with an ISBN number on each issue, 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, Smarandachemulti-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2006-01-01

Total Pages: 140

ISBN-13: 1599730138

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Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!

Book Synopsis Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science by : Florentin Smarandache

Download or read book Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and other areas of science written by Florentin Smarandache and published by Infinite Study. This book was released on 2006-01-01 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either in theoretical exploration or further experiments, while some parts of these problems may be found useful for scholarly stimulation.The present book is also intended for young physics and mathematics fellows who will perhaps find the unsolved problems described here are at least worth pondering. If this book provides only a few highlights of plausible solutions, it is merely to keep the fun of readers in discovering the answers by themselves. Bon voyage!

A First Course in Differential Geometry

Author: Vaisman

Publisher: CRC Press

Published: 1983-12-13

Total Pages: 188

ISBN-13: 9780824770631

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This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.

Book Synopsis A First Course in Differential Geometry by : Vaisman

Download or read book A First Course in Differential Geometry written by Vaisman and published by CRC Press. This book was released on 1983-12-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.

Tensors and Their Applications

Author: Nazrul Islam

Publisher: New Age International

Published: 2006-12

Total Pages: 6

ISBN-13: 8122418384

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The Book Is Written Is In Easy-To-Read Style With Corresponding Examples. The Main Aim Of This Book Is To Precisely Explain The Fundamentals Of Tensors And Their Applications To Mechanics, Elasticity, Theory Of Relativity, Electromagnetic, Riemannian Geometry And Many Other Disciplines Of Science And Engineering, In A Lucid Manner. The Text Has Been Explained Section Wise, Every Concept Has Been Narrated In The Form Of Definition, Examples And Questions Related To The Concept Taught. The Overall Package Of The Book Is Highly Useful And Interesting For The People Associated With The Field.

Book Synopsis Tensors and Their Applications by : Nazrul Islam

Download or read book Tensors and Their Applications written by Nazrul Islam and published by New Age International. This book was released on 2006-12 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Book Is Written Is In Easy-To-Read Style With Corresponding Examples. The Main Aim Of This Book Is To Precisely Explain The Fundamentals Of Tensors And Their Applications To Mechanics, Elasticity, Theory Of Relativity, Electromagnetic, Riemannian Geometry And Many Other Disciplines Of Science And Engineering, In A Lucid Manner. The Text Has Been Explained Section Wise, Every Concept Has Been Narrated In The Form Of Definition, Examples And Questions Related To The Concept Taught. The Overall Package Of The Book Is Highly Useful And Interesting For The People Associated With The Field.