Multilinear Functions of Direction: And Their Uses in Differential Geometry (Classic Reprint) - Hardcover

Eric Harold Neville

Hardcover

ISBN 10: 0267977298 ISBN 13: 9780267977291

Publisher: Forgotten Books, 2018

Synopsis

Delve into multilinear functions of direction and their use in differential geometry to understand curvature and change.

This rigorous work builds from foundational definitions to practical tools for surfaces and their curves.

The book introduces core notions, including how to extend functions off a surface, how rates of change are defined in linear, bilinear, and trilinear forms, and how these relate to geodesic curvature, bilinear curvature, and the Codazzi function. Through careful development of symmetry and relationships, readers see how principal curvatures and principal directions arise from directional analysis.

• Clear definitions and notation for linear, bilinear, and multilinear functions on surfaces
• Techniques for evaluating rates of change along curves and across tangent directions
• Connections between curvature, torsion, and directional derivatives on a surface
• Introductions to the Codazzi function and its role in surface geometry

Ideal for readers seeking a focused, self-contained exploration of direction-based methods in differential geometry.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0267977298
• ISBN 13: 9780267977291
• Binding: Hardcover
• Number of pages: 89