Topics in Differential Geometry

Hanno Rund, William P. Forbes

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780126028508
• eBook ISBN: 9781483272696
• Topic: Technology & Engineering
• Subtopic: Science & Technology Biographies
• Index: Technology & Engineering

Topics in Differential Geometry is a collection of papers related to the work of Evan Tom Davies in differential geometry. Some papers discuss projective differential geometry, the neutrino energy-momentum tensor, and the divergence-free third order concomitants of the metric tensor in three dimensions. Other papers explain generalized Clebsch representations on manifolds, locally symmetric vector fields in a Riemannian space, mean curvature of immersed manifolds, and differential geometry of totally real submanifolds. One paper considers the symmetry of the first and second order for a vector field in a Riemannnian space to arrive at conditions the vector field satisfies. Another paper examines the concept of a smooth manifold-tensor and the three types of connections on the tangent bundle TM, their properties, and their inter-relationships. The paper explains some clarification on the relationship between several related known concepts in the differential geometry of TM, such as the system of general paths of Douglas, the nonlinear connections of Barthel, ano and Ishihara, as well as the nonhomogeneous connection of Grifone. The collection is suitable for mathematicians, geometricians, physicists, and academicians interested in differential geometry.

Table of contents

• Front Cover
• Topics in Differential Geometry
• Copyright Page
• Table of Contents
• List of Contributors
• Preface
• Chapter 1. Evan Tom Davies
• Chapter 2. Reminiscences of E. T. Davies
• Chapter 3. The Uniqueness of the Neutrino Energy-Momentum Tensor and the Einstein-Weyl Equations
• Chapter 4. (G, E) Structures
• Chapter 5. Tensorial Concomitants of an Almost Complex Structure
• Chapter 6. Variétés Symplectiques, Variétés Canoniques, et Systèmes Dynamiques
• Chapter 7. Divergence-Free Third Order Concomitants of the Metric Tensor in Three Dimensions
• Chapter 8. A Functional Equation in the Characterization of Null Cone Preserving Maps
• Chapter 9. Generalized Clebsch Representations on Manifolds
• Chapter 10. Note on Locally Symmetric Vector Fields in a Riemannian Space
• Chapter 11. Mean Curvature of Immersed Manifolds
• Chapter 12. Connections and M-Tensors on the Tangent Bundle TM
• Chapter 13. Differential Geometry of Totally Real Submanifolds