Author Description

Paperback. Pub Date: 2009 08 Pages: 425 Language: English Publisher: World Publishing Company The subject matter of this book had its genesis in Riemanns 1854 habil-itation address: Uber die Hypothesen. welche der Geometrie zu Grundeliegen (On the Hypotheses. which lie at the Foundations of Geometry). Volume II of Spivaks Differential Geometry contains an English translationof this influential lecture. with a commentary by Spivak himself. Riemann. undoubtedly the greatest mathematician of the 19th century. aimed at introducing the notion of a manifold and its structures. The prob-lem involved great difficulties. But. with hypotheses on the smoothness ofthe functions in question. the issues can be settled satisfactorily and thereis now a complete treatment. Traditionally. the structure being focused on is the Riemannian metric. which is a quadratic differential form. Put anot...