Problems And Solutions In Differential Geometry, Lie Series, Differential Forms, Relativity And Applications

This book offers a comprehensive collection of problems and solutions in differential geometry, covering topics like curves, manifolds, and applications in relativity, aimed at students and researchers alike.

"Problems and Solutions in Differential Geometry, Lie Series, Differential Forms, Relativity and Applications" is a comprehensive resource that offers a thorough exploration of differential geometry through a curated collection of problems and solutions. The book caters to both beginners and advanced learners, presenting complex topics in a clear and accessible format. Each section is designed to be self-contained, allowing readers to build their understanding progressively without needing extensive prior knowledge.

The content encompasses a wide range of subjects, including curves, surfaces, Riemannian and pseudo-Riemannian manifolds, and the Hodge duality operator. Additionally, it delves into vector fields, Lie series, differential forms, and matrix-valued differential forms, among others. The inclusion of the Maurer-Cartan form and the Lie derivative further enriches the material, making it relevant for those interested in advanced mathematical concepts.

Beyond the solved problems, the book also features stimulating supplementary exercises and practical software implementations, enhancing the learning experience. The applications discussed range from special and general relativity to Yang-Mills theory, hydrodynamics, and field theory, highlighting the interdisciplinary nature of differential geometry. This volume serves as an invaluable tool not only for students in mathematics, applied mathematics, and theoretical physics but also for researchers seeking to deepen their understanding of the field.