Topological Differential and Conformal Geometry of Surfaces: A Journey into the Curvature of Space

The study of surfaces has intrigued mathematicians for centuries, leading to the development of a rich and intricate body of knowledge known as surface geometry. Topological Differential and Conformal Geometry of Surfaces delves into the heart of this fascinating field, providing a comprehensive exploration of the geometric properties of smooth surfaces.

Topological, Differential and Conformal Geometry of Surfaces (Universitext)

by Jonathan St B T Evans

4.3 out of 5

Language	:	English
File size	:	7455 KB
Screen Reader	:	Supported
Print length	:	296 pages

FREE

Chapter 1: Foundations of Differential Geometry

The book begins by establishing the essential foundations of differential geometry. It introduces fundamental concepts such as differential forms, vector fields, and the exterior derivative, equipping readers with the mathematical tools necessary to navigate the complexities of surface geometry.

Chapter 2: Topology of Surfaces

Chapter 2 explores the topological aspects of surfaces. It delves into the classification of surfaces, revealing their intricate relationships and demonstrating the power of topological invariants in understanding geometric structures.

Chapter 3: Riemannian Geometry of Surfaces

The book then shifts its focus to Riemannian geometry, examining the concept of curvature and its profound implications for surface geometry. Readers will gain a deep understanding of Gaussian, mean, and sectional curvatures, unlocking the secrets of surface shape and behavior.

Chapter 4: Conformal Geometry of Surfaces

Chapter 4 introduces conformal geometry, a specialized branch of geometry that focuses on the preservation of angles. This chapter explores the conformal transformations of surfaces, shedding light on their geometric significance and applications in various fields.

Chapter 5: Applications in Physics and Engineering

To demonstrate the practical relevance of surface geometry, the book devotes a chapter to its applications in physics and engineering. Readers will discover how geometric concepts are used to model physical phenomena, design engineering structures, and solve real-world problems.

Topological Differential and Conformal Geometry of Surfaces concludes with a thought-provoking discussion on the frontiers of research in the field. It highlights open problems and emerging trends, inspiring readers to delve deeper into the captivating world of surface geometry.

Why Choose Topological Differential and Conformal Geometry of Surfaces?

• Comprehensive Coverage: A comprehensive exploration of the geometric properties of smooth surfaces, covering both topological and differential aspects.
• Clear and Accessible Presentation: Written in a clear and accessible style, making complex concepts approachable for students and researchers alike.
• Rigorous Mathematical Framework: Provides a solid mathematical foundation, ensuring a deep understanding of the subject matter.
• Applications in Physics and Engineering: Demonstrates the practical relevance of surface geometry, highlighting its applications in various fields.
• Trusted Universitext Series: Part of the renowned Springer Universitext series, known for its high academic standards and rigorous content.

Target Audience

Topological Differential and Conformal Geometry of Surfaces is an essential resource for:

• Students and researchers in mathematics, particularly in the fields of differential geometry and topology.
• Physicists and engineers interested in the geometric foundations of their fields.
• Anyone with a passion for exploring the beauty and complexity of geometric forms.

Free Download Your Copy Today

Embark on an extraordinary journey into the world of surface geometry. Free Download Topological Differential and Conformal Geometry of Surfaces today and unlock the mysteries of curved surfaces.

Available in paperback and eBook formats.

Topological, Differential and Conformal Geometry of Surfaces (Universitext)

by Jonathan St B T Evans

4.3 out of 5

Language	:	English
File size	:	7455 KB
Screen Reader	:	Supported
Print length	:	296 pages

FREE