If you require a free resource for self-study, several high-quality, legally free textbooks are available online (often under Creative Commons licenses or via university repositories):
: The shortest path between two points on a surface. differential geometry by mittal and agarwal pdf free link
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: Exploration of the first and second fundamental forms, which help define the intrinsic and non-intrinsic curvature of surfaces. He typed the query again, his fingers hovering
by S.C. Mittal and D.C. Agarwal is a comprehensive textbook widely used for undergraduate and postgraduate studies (M.A., M.Sc.) and competitive exams like I.A.S. and P.C.S.. The book focuses on the classical study of curves and surfaces in three-dimensional space using vector methods. Key Content & Topics