M. M. Postnikov Livres

Riemannian geometry is a fundamental area of modern mathematics and is important to the study of relativity. Within the larger context of Riemannian mathematics, the active subdiscipline of geodesics (shortest paths) in Riemannian spaces is of particular significance. This compact and self-contained text by a noted theorist presents the essentials of modern differential geometry as well as basic tools for the study of Morse theory. The advanced treatment emphasizes analytical rather than topological aspects of Morse theory and requires a solid background in calculus. Suitable for advanced undergraduates and graduate students of mathematics, the text opens with a chapter on smooth manifolds, followed by a consideration of spaces of affine connection. Subsequent chapters explore Riemannian spaces and offer an extensive treatment of the variational properties of geodesics and auxiliary theorems and matters.

The first part explores Galois theory, focusing on related concepts from field theory. The second part discusses the solution of equations by radicals, returning to the general theory of groups for relevant facts, examining equations solvable by radicals and their construction, and concludes with the unsolvability by radicals of the general equation of degree n is greater than 5. 1962 edition.

Focusing on geometry, this book presents a comprehensive exploration of affine connection spaces, starting with the properties of geodesics and progressing to covariant derivatives, torsion, and curvature tensors. The English translation includes supplementary chapters summarizing key concepts from manifold and vector bundle theories, enhancing its self-contained nature. Originally structured as lectures, the content has been adapted into chapters for clarity, complete with a new bibliography. This work is part of a larger series on mathematical sciences.