Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches

TL;DR

This book reviews the k-symplectic and k-cosymplectic methods in classical field theories, highlighting their mathematical structures and connections to multisymplectic theory.

Contribution

It provides a comprehensive comparison of k-symplectic and k-cosymplectic approaches and relates them to multisymplectic geometry in classical field theories.

Findings

Clarifies the relationship between k-symplectic, k-cosymplectic, and multisymplectic frameworks.

Summarizes key mathematical structures of first-order classical field theories.

Establishes connections between different geometric approaches in field theory.

Abstract

This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with the multisymplectic theory.