Manifolds - Current Research Areas by Paul Bracken
Manifolds - Current Research Areas - Table of Contents
SECTION 1: HOPF BIFURCATIONS
- 1. Multiple Hopf Bifurcation on Center Manifold
SECTION 2: RELATED TOPICS PERTAINING TO MANIFOLDS
- 2. An Intrinsic Characterization of Bonnet Surfaces
SECTION 3: STUDY OF TYPES OF MANIFOLDS
- 3. Sub-Manifolds of a Riemannian Manifold
- 4. Spectral Theory of Operators on Manifolds
- 5. Symplectic Manifolds & Gromov-Witten Invariants
SECTION 4: MANIFOLDS AND APPLICATIONS
- 6. Head Pose Estimation via Manifold Learning
- 7. A Fusion Scheme of Local Manifold Learning Methods
What You Will Learn in Manifolds - Current Research Areas
Manifolds - Current Research Areas edited by Paul Bracken is an authoritative research collection that highlights the latest theoretical developments and real-world applications of differential manifolds. This comprehensive volume guides readers through center manifolds, Riemannian submanifolds, Gromov-Witten invariants, and local manifold learning with exceptional analytical rigor and depth.
Designed for graduate students, differential geometers, and applied researchers, this foundational volume bridges pure global analysis and data science applications. The contributing authors present detailed mathematical derivations, spectral operator theories, and algorithmic frameworks across 7 specialized research chapters. Whether you are investigating bifurcation theory on center manifolds or studying head pose estimation via non-linear dimension reduction, this volume provides a clear roadmap.
Recognized globally for its broad interdisciplinary coverage, it remains one of the best modern differential geometry books for self-study. By balancing abstract differential topology with applied machine learning techniques, it serves as an essential tool for mastering modern manifold research with confidence.
Book Details & Specifications
Title:
Manifolds - Current Research Areas by Paul Bracken
Publisher:
InTech
Year:
2017
Pages:
164
Type:
PDF
Language:
English
ISBN-10 #:
953512871X
ISBN-13 #:
978-9535128717
License:
CC BY 3.0
Amazon:
Amazon
About the Author: Paul Bracken
The author Paul Bracken
is a distinguished American mathematician and Professor of Mathematics at The University of Texas Rio Grande Valley, internationally recognized for his extensive contributions to mathematical physics, differential geometry, and quantum field theory. He earned his doctorate from the University of Waterloo and has authored hundreds of peer-reviewed research papers and book chapters in pure and applied mathematics.
As editor of Manifolds - Current Research Areas, Bracken assembled leading international experts to showcase the multifaceted utility of manifold theory across physics, geometry, and computer vision. His commitment to rigorous mathematical exposition and interdisciplinary research makes this volume a classic reference for geometric analysis that continues to inspire researchers worldwide.
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