Differential Geometry: Exploring the Curves and Surfaces of Our World

Differential geometry is a captivating and mathematically rigorous field that investigates the geometry of smooth surfaces and manifolds, unlocking profound insights into the structures and behaviors of our universe. This comprehensive book serves as an invaluable guide for students, researchers, and practitioners seeking to delve into the intricacies and applications of differential geometry.

With meticulous attention to detail and clarity, this book elucidates the fundamental concepts, powerful techniques, and captivating applications of differential geometry. Embark on a journey through the world of curves and surfaces, exploring their tangent spaces and differential maps, before venturing into the realm of Riemannian geometry and its applications in physics and engineering.

Discover the elegance and significance of symplectic geometry, unraveling its intricate relationship with Hamiltonian mechanics and classical field theory. Delve into Kähler geometry, a specialized branch with profound implications in algebraic geometry and complex analysis.

Explore the topological landscapes of differential topology, uncovering the intricacies of differential forms, cohomology, and characteristic classes. Witness the harmonious interplay between differential geometry and analysis in geometric analysis, where Sobolev spaces, heat kernels, and index theorems converge to unveil hidden structures and connections.

This book is a testament to the enduring fascination with differential geometry, showcasing its profound impact on diverse fields, ranging from physics and engineering to computer graphics and artificial intelligence. With its comprehensive coverage and accessible presentation, this book empowers readers to unlock the mysteries of differential geometry and embark on a transformative intellectual journey.

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Publisher ‏: ‎ PageBook24.com (January 13, 2025)
Language : ‎ English
Dimensions ‏: ‎ 6 x 9 inches
Pages ‏: ‎ 172 pages

Pasquale De Marco stands as a prolific author whose literary prowess knows no bounds. With a passion for storytelling that transcends genres, he has made a name for himself as a versatile writer with the extraordinary ability to captivate readers across diverse literary landscapes. His journey as an author is marked by an insatiable curiosity, a love for the written word, and a relentless commitment to sharing knowledge and experiences with the world.

Pasquale De Marco collaborates with a dedicated team of ghostreaders who assist him in evaluating and editing the manuscripts. His collaborators are not only skilled professionals but also avid readers who purchase and read books as a personal hobby. This unique blend of creativity allows Pasquale to push the boundaries of traditional publishing, making literature more accessible and diverse.