Andrejić V. Geometry: Smooth Manifolds, Pseudo-Riemannian Geometry, Osserman Manifolds

Belgrade (Serbia): Faculty of Mathematics, 2023. - 235 p.This book is meant to be a monograph on Osserman manifolds and brings together a large number of results published by the author in this topic. In order for as many readers as possible to follow these results, the book also contains a detailed introduction to smooth manifolds, as well as the basics of Riemannian and pseudo-Riemannian geometry, and can be used as a textbook for the course in differential geometry. The book can be divided into three imaginary parts: Part I Smooth manifolds, consisting of chapters 1–4, Part II Pseudo-Riemannian geometry, consisting of chapters 5–8, and Part III Osserman manifolds, consisting of chapters 9–11.Preface.
Smooth manifolds and maps.
Tangent vectors and maps.
Vector fields and bundles.
Tensor fields.
Pseudo-Riemannian metric.
Connection.
Curvature.
More pseudo-Riemannian geometry.
Osserman conditions.
Duality principle.
Osserman tensors and manifolds.
A Appendix.
Bibliography.
Index.True PDF (A4 format)