Multiplicative Differential Geometry
暫譯: 乘法微分幾何

Georgiev, Svetlin G.

Multiplicative Differential Geometry
  • 出版商: CRC
  • 出版日期: 2022-07-20
  • 售價: $4,720
  • 貴賓價: 9.5 折 $4,484
  • 語言: 英文
  • 頁數: 360
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1032290609
  • ISBN-13: 9781032290607

    • 海外代購書籍(需單獨結帳)

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商品描述

This book introduces multiplicative Frenet curves. We define multiplicative tangent, multiplicative normal, and multiplicative normal plane for a multiplicative Frenet curve. We investigate the local behaviours of a multiplicative parameterized curve around multiplicative biregular points, define multiplicative Bertrand curves and investigate some of their properties. A multiplicative rigid motion is introduced.

The book is addressed to instructors and graduate students, and also specialists in geometry, mathematical physics, differential equations, engineering, and specialists in applied sciences. The book is suitable as a textbook for graduate and under-graduate level courses in geometry and analysis. Many examples and problems are included.

The author introduces the main conceptions for multiplicative surfaces: multiplicative first fundamental form, the main multiplicative rules for differentiations on multiplicative surfaces, and the main multiplicative regularity conditions for multiplicative surfaces. An investigation of the main classes of multiplicative surfaces and second fundamental forms for multiplicative surfaces is also employed. Multiplicative differential forms and their properties, multiplicative manifolds, multiplicative Einstein manifolds and their properties, are investigated as well.

Many unique applications in mathematical physics, classical geometry, economic theory, and theory of time scale calculus are offered.

商品描述(中文翻譯)

本書介紹了乘法弗雷內曲線（multiplicative Frenet curves）。我們為乘法弗雷內曲線定義了乘法切線（multiplicative tangent）、乘法法線（multiplicative normal）和乘法法平面（multiplicative normal plane）。我們研究了乘法參數化曲線在乘法雙正則點（multiplicative biregular points）附近的局部行為，定義了乘法伯特蘭曲線（multiplicative Bertrand curves）並探討其一些性質。書中還介紹了乘法剛性運動（multiplicative rigid motion）。

本書適合教師、研究生以及幾何學、數學物理、微分方程、工程學和應用科學的專家。該書適合作為幾何學和分析學的研究生及本科生課程的教科書，並包含許多範例和習題。

作者介紹了乘法曲面（multiplicative surfaces）的主要概念：乘法第一基本形式（multiplicative first fundamental form）、乘法曲面上的主要乘法微分法則（main multiplicative rules for differentiations on multiplicative surfaces）以及乘法曲面的主要乘法正則性條件（main multiplicative regularity conditions for multiplicative surfaces）。本書還探討了乘法曲面的主要類別及其第二基本形式（second fundamental forms for multiplicative surfaces）。此外，乘法微分形式（multiplicative differential forms）及其性質、乘法流形（multiplicative manifolds）、乘法愛因斯坦流形（multiplicative Einstein manifolds）及其性質也一併研究。

本書提供了在數學物理、古典幾何、經濟理論和時間尺度微積分理論中的許多獨特應用。

作者簡介

Svetlin G. Georgiev is a mathematician who has worked in various areas of the study. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales. He is also the author of Dynamic Geometry of Time Scales, CRC Press. He is a co-author of Conformable Dynamic Equations on Time Scales, with Douglas R. Anderson, and also: Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDE; Boundary Value Problems on Time Scales, Volume 1 and Volume II, all with Khalid Zennir and published by CRC Press.

作者簡介(中文翻譯)

Svetlin G. Georgiev 是一位數學家，曾在多個研究領域工作。他目前專注於調和分析、泛函分析、偏微分方程、常微分方程、Clifford 和四元數分析、積分方程以及時間尺度上的動態微積分。他也是《Dynamic Geometry of Time Scales》的作者，該書由 CRC Press 出版。他與 Douglas R. Anderson 共同撰寫了《Conformable Dynamic Equations on Time Scales》，此外還有與 Khalid Zennir 共同撰寫的《Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDE; Boundary Value Problems on Time Scales, Volume 1》和《Volume II》，均由 CRC Press 出版。

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