Leseprobe
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Lie Equations, Vol. I
Donald Clayton Spencer, Antonio Kumpera
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Endomorphism, Jacobian matrix and determinant, J-invariant, Volume element, Differential structure, Equation, Pseudogroup, Vector bundle, Differential operator, Vector field, Tangent bundle, Complex conjugate, Morphism, Derivative, Special case, Frobenius theorem (real division algebras), Parameter, Linear map, Nonlinear system, Structure tensor, Adjoint representation, Exponential function, Exterior derivative, Automorphism, Tangent vector, Groupoid, Subgroup, Theorem, Fiber bundle, Pseudo-differential operator, Fibration, Tangent space, Homeomorphism, Subcategory, Tensor field, Associative algebra, Subset, Exactness, Variable (mathematics), Coefficient, Model category, Riemann surface, Manifold, Sheaf (mathematics), Submanifold, Partial differential equation, Torsion tensor, Complex manifold, Partial derivative, Presheaf (category theory), Diffeomorphism, Pointwise, Differentiable function, Subalgebra, Open set, Cauchy–Riemann equations, Affine transformation, Existential quantification, Big O notation, Cotangent bundle, Differential form, Linear combination, Exponential map (Riemannian geometry), Tensor product, Vector space, Complex group, Right inverse, Frobenius theorem (differential topology), Analytic function, Holomorphic function