**Natural Operations in Differential Geometry**

by Ivan Kolar, Peter W. Michor, Jan Slovak

**Publisher**: Springer 1993**ISBN/ASIN**: 3540562354**ISBN-13**: 9783540562351**Number of pages**: 437

**Description**:

This book tries to be a rather comprehensive textbook on all basic structures from the theory of jets which appear in different branches of differential geometry. The book begins with an introduction to differential geometry stressing naturality and functionality, and the general theory of connections on arbitrary fibered manifolds. The functional approach to classical natural bundles is extended to a large class of geometrically interesting categories. Several methods of finding all natural operators are given and these are identified for many concrete geometric problems. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces, and the basic structures from the theory of jets are therefore described here too in a self-contained manner.

Download or read it online for free here:

**Download link**

(2.8MB, PDF)

## Similar books

**Comparison Geometry**

by

**Karsten Grove, Peter Petersen**-

**Cambridge University Press**

This volume is an up-to-date panorama of Comparison Geometry, featuring surveys and new research. Surveys present classical and recent results, and often include complete proofs, in some cases involving a new and unified approach.

(

**6864**views)

**Lectures on Minimal Surface Theory**

by

**Brian White**-

**arXiv**

The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.

(

**3842**views)

**Noncompact Harmonic Manifolds**

by

**Gerhard Knieper, Norbert Peyerimhoff**-

**arXiv**

We provide a survey on recent results on noncompact simply connected harmonic manifolds, and we also prove many new results, both for general noncompact harmonic manifolds and for noncompact harmonic manifolds with purely exponential volume growth.

(

**3318**views)

**Lectures on Exterior Differential Systems**

by

**M. Kuranishi**-

**Tata Institute of Fundamental Research**

Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.

(

**7103**views)