Differential Geometry
Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)
English | 2025 | ISBN: 9819616301 | 604 Pages | PDF EPUB (True) | 52 MB
English | 2025 | ISBN: 9819616301 | 604 Pages | PDF EPUB (True) | 52 MB
This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG). Starting with the basics of semi-Riemannian geometry, the book aims to develop the understanding of smooth 1-parameter variations of geodesics of, and correspondingly of, Jacobi fields. A few algebraic aspects required by the treatment of the Riemann–Christoffel four-tensor and sectional curvature are successively presented. Ricci curvature and Einstein manifolds are briefly discussed. The Sasaki metric on the total space of the tangent bundle over a Riemannian manifold is built, and its main properties are investigated. An important integration technique on a Riemannian manifold, related to the geometry of geodesics, is presented for further applications. The other three books of the series are