Differential geometry is a branch of mathematics that investigates smooth manifolds, using a wide range of techniques from mathematical analysis and linear algebra. Differential geometry plays a fundamental role in mathematical physics. For instance, general relativity is the theory of space, time, and gravity formulated by Einstein using the methods of differential geometry. Thus, the Universe appears a differentiable manifold endowed with a semi-Riemannian metric, describing the curvature of the spacetime. Later, differential geometry was used by physicists as a key ingredient in developing the quantum field theory and the standard model of particle physics. Moreover, in many other fields of physics, such as electromagnetism, Lagrangian and Hamiltonian mechanics, black holes and geometrothermodynamics, the tools of differential geometry are essential, since all these need curved spaces for the description of various physical systems.
The main goal of the current Research Topic is to cover novel trends concerning differential geometric methods used in modern theories of physics. Developing new concepts and techniques in the theory of manifolds equipped with remarkable geometric structures, as well as obtaining new results with relevance in theoretical physics, are the first aim of this volume. The second aim is to attract high-quality survey papers on the same topics written by leading experts in the field; such kind of articles must not only summarize historical facts and the state-of-the-art knowledge about the topic under investigation, but also must propose some challenging problems, thus stimulating further studies in the field. The third aim of the volume is to collect valuable research articles presenting direct and important applications of differential geometric techniques to theoretical physics.
All submitted contributions should use a differential geometric treatment and must either include applications in physics or provide irrefutable evidence of potential applications. We welcome Original Research, Review, Mini Review and Perspective articles on themes including, but not limited to:
• Differential geometry of manifolds and submanifolds
• Symmetries of geometric structures
• Geometric theories of gravitation
Differential geometry is a branch of mathematics that investigates smooth manifolds, using a wide range of techniques from mathematical analysis and linear algebra. Differential geometry plays a fundamental role in mathematical physics. For instance, general relativity is the theory of space, time, and gravity formulated by Einstein using the methods of differential geometry. Thus, the Universe appears a differentiable manifold endowed with a semi-Riemannian metric, describing the curvature of the spacetime. Later, differential geometry was used by physicists as a key ingredient in developing the quantum field theory and the standard model of particle physics. Moreover, in many other fields of physics, such as electromagnetism, Lagrangian and Hamiltonian mechanics, black holes and geometrothermodynamics, the tools of differential geometry are essential, since all these need curved spaces for the description of various physical systems.
The main goal of the current Research Topic is to cover novel trends concerning differential geometric methods used in modern theories of physics. Developing new concepts and techniques in the theory of manifolds equipped with remarkable geometric structures, as well as obtaining new results with relevance in theoretical physics, are the first aim of this volume. The second aim is to attract high-quality survey papers on the same topics written by leading experts in the field; such kind of articles must not only summarize historical facts and the state-of-the-art knowledge about the topic under investigation, but also must propose some challenging problems, thus stimulating further studies in the field. The third aim of the volume is to collect valuable research articles presenting direct and important applications of differential geometric techniques to theoretical physics.
All submitted contributions should use a differential geometric treatment and must either include applications in physics or provide irrefutable evidence of potential applications. We welcome Original Research, Review, Mini Review and Perspective articles on themes including, but not limited to:
• Differential geometry of manifolds and submanifolds
• Symmetries of geometric structures
• Geometric theories of gravitation
