Riemannian geometry /

Differential geometry is a beautifully elegant subject that is also uncompromisingly technical in its language. This book is a translation from the Portuguese of the second edition of the author's Geometria Riemanniana (Rio de Janeiro, Brazil, 1988) and is appropriate for graduate students studying the techniques and fundamental theorems of Riemannian geometry. In his presentation, Do Carmo effectively strikes a delicate balance between the Byzantine nature of local coordinate computations and the stark austerity of the more modern invariant approach to differential geometry. The result is a solid, readable (though demanding) book full of wonderful mathematical taste. Exercises abound and there is an extensive bibliography. No doubt destined to become a standard reference in the field. Highly recommended for advanced undergraduates, graduate students, and professionals.-S. J. Colley, Oberlin College