Lie Equations, Vol. I General Theory

In this monograph the authors redevelop the theory systematically using two different approaches. A general mechanism for the deformation of structures on manifolds was developed by Donald Spencer ten years ago. A new version of that theory, based on the differential calculus in the analytic spaces of Grothendieck, was recently given by B. Malgrange. The first approach adopts Malgrange's idea in defining jet sheaves and linear operators, although the brackets and the non-linear theory arc treated in an essentially different manner. The second approach is based on the theory of derivations, and its relationship to the first is clearly explained. The introduction describes examples of Lie equations and known integrability theorems, and gives applications of the theory to be developed in the following chapters and in the subsequent volume.

About the author

Antonio Kumpera & Donald Clayton Spencer

Summary

As the title indicates, the content of these notes is a lengthy construction of techniques devised to study specific differential geometric problems. In this introduction we state our main objectives and illustrate by examples some of their geometric implications.

Product details

• Authors: Antonio Kumpera, Donald D. Spencer, Donald Clayton Spencer, John N. Mather, Donald Spencer, Kumpera Antonio, Spencer Donald Clayton
• Assisted by: Elias Stein (Editor), Phillip Griffiths (Editor)
• Publisher: University Presses
• Content: Book
• Product form: Paperback / Softback
• Publication date: 21.10.1972
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra
• EAN: 9780691081113
• ISBN: 978-0-691-08111-3
• Pages: 309
• Dimensions (packing): 15.2 x 22.9 cm
• Weight (packing): 454 g
• Series: Annals of Mathematics Studies > 73; Annals of Mathematics Studies
• Subjects: Algebra, Parameter, MATHEMATICS / Algebra / General, Theorem, Derivative, Manifold, equation, exactness, Pseudo-Differential Operator, Partial differential equation, submanifold, diffeomorphism, vector bundle, Vector space, differential operator, Morphism, tangent bundle, nonlinear system, Tensor field, fiber bundle, Tangent Space, holomorphic function, Complex manifold, Riemann surface, Tensor Product, groupoid, Vector field, automorphism, analytic function, special case, associative algebra, differential form, Variable (mathematics), Partial derivative, coefficient, Subset, Subgroup, Big O notation, Open set, Sheaf (mathematics), Subalgebra, Linear Map, Existential quantification, Linear combination, Presheaf (category theory), Model category, Fibration, Differentiable function, Jacobian matrix and determinant, Endomorphism, Cauchy–Riemann equations, Pointwise, Affine transformation, Exterior derivative, Complex conjugate, Right inverse, Exponential function, Adjoint representation, Homeomorphism, Tangent vector, Frobenius theorem (differential topology), Frobenius theorem (real division algebras), Exponential map (Riemannian geometry), Volume element, Pseudogroup, Subcategory, J-invariant, Cotangent bundle, Torsion tensor, Differential structure, Structure tensor, Complex group