Conformal Differential Geometry and Its Generalizations

Comprehensive coverage of the foundations, applications, recentdevelopments, and future of conformal differential geometry

Conformal Differential Geometry and Its Generalizations is thefirst and only text that systematically presents the foundationsand manifestations of conformal differential geometry. It offersthe first unified presentation of the subject, which wasestablished more than a century ago. The text is divided into sevenchapters, each containing figures, formulas, and historical andbibliographical notes, while numerous examples elucidate thenecessary theory.

Clear, focused, and expertly synthesized, Conformal DifferentialGeometry and Its Generalizations
∗ Develops the theory of hypersurfaces and submanifolds of anydimension of conformal and pseudoconformal spaces.
∗ Investigates conformal and pseudoconformal structures on amanifold of arbitrary dimension, derives their structure equations,and explores their tensor of conformal curvature.
∗ Analyzes the real theory of four–dimensional conformal structuresof all possible signatures.
∗ Considers the analytic and differential geometry of Grassmann andalmost Grassmann structures.
∗ Draws connections between almost Grassmann structures and webtheory.

Conformal differential geometry, a part of classical differentialgeometry, was founded at the turn of the century and gave rise tothe study of conformal and almost Grassmann structures in lateryears. Until now, no book has offered a systematic presentation ofthe multidimensional conformal differential geometry and theconformal and almost Grassmann structures.

After years of intense research at their respective universitiesand at the Soviet School of Differential Geometry, Maks A. Akivisand Vladislav V. Goldberg have written this well–conceived,expertly executed volume to fill a void in the literature. Dr.Akivis and Dr. Goldberg supply a deep foundation, applications,numerous examples, and recent developments in the field. Many ofthe findings that fill these pages are published here for the firsttime, and previously published results are reexamined in a unifiedcontext.

The geometry and theory of conformal and pseudoconformal spaces ofarbitrary dimension, as well as the theory of Grassmann and almostGrassmann structures, are discussed and analyzed in detail. Thetopics covered not only advance the subject itself, but poseimportant questions for future investigations. This exhaustive,groundbreaking text combines the classical results and recentdevelopments and findings.

This volume is intended for graduate students and researchers ofdifferential geometry. It can be especially useful to thosestudents and researchers who are interested in conformal andGrassmann differential geometry and their applications totheoretical physics.