Extrinsic Geometry of Foliations

This book explores geometric problems of foliation theory, focusing on extrinsic geometry and mixed curvature. It discusses integral and variation formulas, curvature and dynamics, and various methods for solving foliation problems, including integral and variation formulas, extrinsic geometric flows, and computable Finsler metrics. It is designed for newcomers and experienced geometers and can serve as a valuable resource for researchers in differential equations and their applications.

Format: Paperback / softback
Length: 319 pages
Publication date: 24 May 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the intricate realm of geometric problems related to foliation theory, with a special focus on extrinsic geometry, a modern branch of Riemannian Geometry. At the heart of the discussion lies the concept of mixed curvature, which plays a pivotal role. The book explores a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations, shedding light on its intricate details.

Organized into five chapters, the book covers a wide range of topics. It delves into integral and variation formulas, providing valuable tools for understanding the curvature and dynamics of foliations. Different approaches and methods, ranging from local to global, regular to singular, are described using these formulas, along with extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and computable Finsler metrics.

The book serves as a valuable resource for both newcomers to the field and experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a diverse array of researchers in differential equations and their applications. It provides a comprehensive overview of the state-of-the-art in geometric and analytical theory of foliations, showcasing the authors' extensive expertise in extrinsic geometry.

With its clear and concise writing style, the book is designed to be accessible to a broad audience. It serves as an excellent introduction to the subject, while also offering insights and advanced techniques for those seeking to deepen their understanding of foliation theory and its applications. Moreover, it can inspire new and exciting research directions, making it a valuable supplement to postgraduate-level work and a source of inspiration for scholars and researchers alike.

Weight: 516g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030700690
Edition number: 1st ed. 2021