Title: Multilinear Functions of Direction: And Their Uses in Differential Geometry (Classic Reprint)
Publisher: Forgotten Books
Publication Date: 2019
Language: English
ISBN 10: 0267977298
ISBN 13: 9780267977291
Binding: HRD
Condition: New
Weight: 324 grams

About this title

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.

"About this title" may belong to another edition of this title.

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