Lectures on Geodesics in Riemannian Geometry
by M. Berger
Publisher: Tata Institute of Fundamental Research 1965
Number of pages: 317
The main topic of these notes is geodesics. Our aim is 1) to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it and 2) to give global results for Riemannian manifolds which are subject to geometric conditions of various types; these conditions involve essentially geodesics.
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by Ilkka Holopainen, Tuomas Sahlsten
Based on the lecture notes on differential geometry. From the contents: Differentiable manifolds, a brief review; Riemannian metrics; Connections; Geodesics; Curvature; Jacobi fields; Curvature and topology; Comparison geometry; The sphere theorem.
by Curtis McMullen - Harvard University
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; etc.
by Bang-Yen Chen - arXiv
Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. In this book, the author provides a broad review of Riemannian submanifolds in differential geometry.
by D. Bao, R. Bryant, S. Chern, Z. Shen - Cambridge University Press
Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. The contributors consider issues related to volume, geodesics, curvature, complex differential geometry, and parametrized jet bundles.