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Название: Variational Problems in Geometry (Translations of Mathematical Monographs)
Автор: Nishikawa S.
The reason why I wanted to read this book was to learn about Geodesics in a very short time. This book is ideal for such a study and beyond. The Appendix on Theory of Manifolds alone is a good read for a beginner and gives enough details on Manifolds to start reading the book.