Open access peer-reviewed Edited Volume

Manifolds - Recent Developments and Applications

Paul Bracken

The University of Texas Rio Grande Valley

Professor Paul Bracken obtained his BSc degree from the University of Toronto and holds a Ph.D. from the University of Waterloo in Canada. His research interests include mathematical problems from the area of quantum mechanics and quantum field theory, differential geometry, a study of partial differential equations as well as their overlap with other problems in physics. He has published more than 180 papers in journals and books and has given many talks at different levels over the years.

Covering

Covariant Derivative Connection Elliptic Boundary Value Problem Hodge Decomposition Differential Form Curvature Metric Spin Structure Bundle Local Index Theorem Clifford Algebra

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About the book

Manifolds, a subject of interest for researchers in their own right, have many applications and interactions with many areas of mathematics and physics. These areas include partial differential equations, elliptic problems, boundary value problems, Schrodinger, and heat operators. Fundamentally, with Descartes and the introduction of coordinates, a line or a plane becomes via coordinates an algebraic object, more precisely an equation.

In general, any coordinates replace geometry by algebra and we get a two-dimensional correspondence between the study of space and the study of equations. This process is a shift from geometry to numbers at a basic level. The coordinatization process has been used well before mathematicians accepted it as a method.

The manifolds are precisely those spaces that can be piecewise provided with coordinates by means of a smooth correspondence on overlaps, and the book will intend to study these structures in mathematics, as well as the impact and applications to a variety of other areas of mathematics. Recently, there have been very deep insights into the subject, and it is intended this the book will provide readers with an interest in the subject a clear review of advances and consequences in this area of investigation.

Publishing process

Book initiated and editor appointed

Date completed: February 9th 2022

Applications to edit the book are assessed and a suitable editor is selected, at which point the process begins.

Chapter proposals submitted and reviewed

Deadline Extended: Open for Submissions

Potential authors submit chapter proposals ready for review by the academic editor and our publishing review team.

Approved chapters written in full and submitted

Deadline for full chapters: June 11th 2022

Once approved by the academic editor and publishing review team, chapters are written and submitted according to pre-agreed parameters

Full chapters peer reviewed

Review results due: August 30th 2022

Full chapter manuscripts are screened for plagiarism and undergo a Main Editor Peer Review. Results are sent to authors within 30 days of submission, with suggestions for rounds of revisions.

Book compiled, published and promoted

Expected publication date: October 29th 2022

All chapters are copy-checked and typesetted before being published. IntechOpen regularly submits its books to major databases for evaluation and coverage, including the Clarivate Analytics Book Citation Index in the Web of ScienceTM Core Collection. Other discipline-specific databases are also targeted, such as Web of Science's BIOSIS Previews.

About the editor

Paul Bracken

The University of Texas Rio Grande Valley

Professor Paul Bracken is currently a Professor in the Department of Mathematics, at the University of Texas RGV in Edinburg, TX. He obtained his BSc degree from the University of Toronto and holds a Ph.D. from the University of Waterloo in Canada. His research interests include mathematical problems from the area of quantum mechanics and quantum field theory, differential geometry, a study of partial differential equations as well as their overlap with other problems in physics. He has published more than 180 papers in journals and books and has given many talks at different levels over the years. This is the seventh volume he has worked on with IntechOpen publishers.

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Book chapters authored 9

Books edited 7

Introducing your Author Service Manager

Ms. Ana Javor

As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors, and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact.

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