Manifolds, tensor analysis

Abstract The fibre derivative of a bundle map is studied in detail. In the particular case of a real function, several constructions useful to study singular lagrangians are presented.

Some … Expand. Symplectic connections and the linearisation of Hamiltonian systems. This paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an … Expand.

Lagrangian description, symplectization, and Eulerian dynamics of incompressible fluids. Eulerian dynamical equations in a three-dimensional domain are used to construct a formal symplectic structure on time-extended space. Symmetries, invariants, and conservation laws are related to … Expand. View 5 excerpts, cites methods and background. Differential calculus on manifolds with boundary applications. This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states.

A geometrically inspired way of dealing with these kind of … Expand. View 1 excerpt, cites background. On the assumption that the Riemannian curvature and its variation over space—time are small enough and using an explicit expression for the inertia tensor defined by Dixon in his approach to describe … Expand.

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Create a free Team What is Teams? Learn more. Classical tensor analysis and Tensors on Manifolds Ask Question. Asked 7 years, 4 months ago. Active 6 years, 11 months ago. Viewed 1k times. Thank you. Add a comment. Active Oldest Votes.

Thomas Thomas Daniel Mahler Daniel Mahler 1, 13 13 silver badges 26 26 bronze badges. I recently got Lee's texts on Smooth Manifolds and Riemannian Geometry and am making my way through them albeit slowly. Spivak's multivolume tome was a bit too forbidding.

Sign up or log in Sign up using Google. An introductory chapter establishes notation and explains various topics in set theory and topology. Chapters 1 and 2 develop tensor analysis in its function-theoretical and algebraic aspects, respectively.

The next two chapters take up vector analysis on manifolds and integration theory. In the last two chapters 5 and 6 several important special structures are studied, those in Chapter 6 illustrating how the previous material can be adapted to clarify the ideas of classical mechanics.

The text as a whole offers numerous examples and problems. A student with a background of advanced calculus and elementary differential equation could readily undertake the study of this book.