nptel.ac.in
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NPTEL is a government-backed online learning platform offering free and paid courses from Indian institutes, featuring video lectures, downloadable lecture notes, assignments, and certificates. It hosts mathematics and engineering courses, including topics in differential geometry and Riemannian metrics.
More resources on Riemannian Metrics
nLab: Riemannian Geometry
Comprehensive wiki entry with references.
John M. Lee Book Companion
Free sample chapters and errata for Riemannian Manifolds.
Differential Geometry
Explore Riemannian metrics & differential geometry with MIT's George Lusztig. Learn key concepts in this comprehensive course.
Lectures on Riemannian Geometry
Explore Riemannian metrics with Frederic Schuller's "Lectures on Riemannian Geometry." Learn the foundations in this comprehensive course!
mathworld.wolfram.com
MathWorld is an extensive online encyclopedia of mathematics from Wolfram that provides detailed, readable articles on mathematical concepts, definitions, and theorems. It covers topics from algebra and geometry to differential geometry (including Riemannian metrics), offering formulas, examples, and references.
Riemannian Geometry
Riemannian Geometry - A book resource