Riemannian Geometry
Metrics, geodesics, curvature tensors, and comparison theorems.
Riemannian Geometry. Metrics, geodesics, curvature tensors, and comparison theorems.
Foundations and canonical references
The standard treatments of riemannian geometry approach the subject from complementary angles. Docarmo, Riemannian Geometry (1992) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Petersen, Riemannian Geometry (2016) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for riemannian geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1992Riemannian Geometrydocarmo-1992
- textbook · primary · 2016Riemannian Geometrypetersen-2016
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