Abstract
This chapter contains a 56-page-long list of formulae from the calculus on manifolds, and tables concerning different topics: Lie groups, Lie algebras and symmetric spaces, a list of Poincaré polynomials of compact simple Lie groups, an overview of real forms of classical complex simple Lie algebras and their corresponding simple Lie groups, a table of irreducible Riemannian symmetric spaces of type I and III, a table of Riemannian symmetric spaces of classical type with noncompact isotropy group, etc. One can find the formulae for Christoffel symbols, the curvature tensor, Bianchi identities, Ricci tensor, the basic differential operators, the expression for conformal changes of Riemannian metrics, Cartan structure equations for pseudo-Riemannian manifolds, and many more. Several of these formulae are used throughout the book; others are not, but they have been included since such a collection might prove useful as an aide-mémoire, also to lecturers and researchers.
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Notes
- 1.
The isotropy groups for each group G are listed under it. In all cases but for Sp(n,ℂ) and Sp(n,ℝ), the expression of the first listed isotropy group has been broken in two lines.
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Gadea, P.M., Muñoz Masqué, J., Mykytyuk, I.V. (2013). Some Formulas and Tables. In: Analysis and Algebra on Differentiable Manifolds. Problem Books in Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5952-7_7
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DOI: https://doi.org/10.1007/978-94-007-5952-7_7
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