8 edition of **Vector fields and other vector bundle morphisms** found in the catalog.

- 78 Want to read
- 33 Currently reading

Published
**1981**
by Springer-Verlag in Berlin, New York
.

Written in English

- Vector bundles.,
- Vector fields.,
- Singularities (Mathematics)

**Edition Notes**

Statement | Ulrich Koschorke. |

Series | Lecture notes in mathematics ;, 847, Lecture notes in mathematics (Springer-Verlag) ;, 847. |

Classifications | |
---|---|

LC Classifications | QA3 .L28 no. 847, QA612.63 .L28 no. 847 |

The Physical Object | |

Pagination | 304 p. ; |

Number of Pages | 304 |

ID Numbers | |

Open Library | OL4259043M |

ISBN 10 | 0387105727 |

LC Control Number | 81004610 |

Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie groups, symmetric spaces, and symplectic and Hermitian vector bundles. A consideration of other differential geometric structures concludes the text, including surveys of characteristic classes of principal bundles, Cartan connections Reviews: 9. On sectioning tangent bundles and other vector bundles, Rend. Circ. Mat. Palermo (2) Suppl. 96 (), 85– Google Scholar [12] KOSCHORKE, U.: Vector fields and other vector bundle morphisms — a singularity approach, Lecture Notes in Math. , Springer, Berlin, Google Scholar.

commutes, that is, ∘ = ∘.In other words, is fiber-preserving, and f is the induced map on the space of fibers of E: since π E is surjective, f is uniquely determined a given f, such a bundle map is said to be a bundle map covering f.. Relation between the two notions. It follows immediately from the definitions that a bundle map over M (in the first sense) is the same thing as a. In this article we give a vanishing result for Dolbeault cohomology groups \({H^{p,q}(X, S^{\nu}E\otimes L)}\), where ν is a positive integer, E is a vector bundle generated by sections and L is.

The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. Here is a provisional Table of Contents. At present only about half of the book is in good enough shape to be posted online, approximately pages. And what a vector field is, is its pretty much a way of visualizing functions that have the same number of dimensions in their input as in their output. So here I'm gonna write a function that's got a two dimensional input X and Y, and then its output is going to be a two dimensional vector and each of the components will somehow depend on X and Y.

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Buy Vector Fields and Other Vector Bundle Morphisms - A Singularity Approach (Lecture Notes in Mathematics) on FREE SHIPPING on qualified orders Vector Fields and Other Vector Bundle Morphisms - A Singularity Approach (Lecture Notes in Mathematics): Koschorke, Ulrich: : BooksCited by: Vector Fields and Other Vector Bundle Morphisms — A Singularity Approach.

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[U Koschorke]. Vector fields and other vector bundle morphisms. Berlin ; New York: Springer-Verlag, (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: U Koschorke. COVID Resources.

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Vector fields and other vector bundle morphisms. Berlin ; New York: Springer-Verlag, (DLC) (OCoLC) Print version: Koschorke, U.

(Ulrich), Vector fields and other vector bundle morphisms. Berlin ; New York: Springer-Verlag, (OCoLC) Material Type: Document, Internet resource: Document Type. Cite this chapter as: Koschorke U.

() Introduction. In: Vector Fields and Other Vector Bundle Morphisms — A Singularity Approach. Lecture Notes in Mathematics, vol Cite this chapter as: Koschorke U. () Existence and homotopy classification.

In: Vector Fields and Other Vector Bundle Morphisms — A Singularity Approach. Purchase Introduction to Global Variational Geometry, Volume - 1st Edition.

Print Book & E-Book. ISBNVector Fields and Other Vector Bundle Morphisms — A Singularity Approach; Vector Fields on Manifolds; Vector Generalized Linear and Additive Models; Vector Lattices and Integral Operators; Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems; Vector Measures, Integration and Related Topics; Vector Network Analyzer (VNA.

Definition The vector bundle isomorphism γ: π-1 T(M)-> V = Ker(dπ) is called the vertical lift. For each section s: T(M)-> π-1 T(M) the vertical vector field γs is the vertical lift of s. Note that in general s may fail to be the natural lift of a vector field on M.

Vector bundle morphisms. A morphism from the vector bundle π 1: E1 → X1 to the vector bundle π 2: E2 → X2 is given by a pair of continuous maps f: E1 → E2 and g: X1 → X2 such that.

g ∘ π 1 = π 2 ∘ f. for every x in X1, the map π 1−1 ({ x }) → π 2−1 ({ g (x)}) induced by f. Given a differentiable manifold, a vector field on is an assignment of a tangent vector to each point in. More precisely, a vector field is a mapping from into the tangent bundle so that ∘ is the identity mapping where denotes the projection from other words, a vector field is a section of the tangent bundle.

An alternative definition: A smooth vector field on a manifold is a linear. where is the zero vector bundle, is exact if is a monomorphism, is an epimorphism set of vector bundles over and -morphisms of locally constant rank forms an exact subcategory of the category.

For any vector bundle and mapping, the induced fibre bundle is endowed with a vector bundle structure such that the morphism is a vector bundle morphism. Supermanifolds and vector bundles.

Let M0 be a manifold, and E be a vector bundle on M0. Then we can deﬁne the supermanifold M:= Tot(ΠE), the total space of E with changed parity. Namely, the reduced manifold of M is 0, and structure sheaf C∞ theis sections of ΛE∗. Vertical Vectors, Horizontal Forms Fibrations Sections of Fibered Manifolds Vector Bundles Vector Bundle Morphisms Inverse Image of a Vector Bundle Notes and Additional Topics Chapter 2: Analysis on Manifolds; Vector Fields Vector Fields Koschorke, Vector Fields and other Vector Bundle Morphisms - A Singularity Approach, Lecture Notes in Mathematics (Springer, Berlin, ).

[8] M.E. Mahowald, The index of a tangent 2-field, Pacific J. Math. 58 () [9]. The notion of vector bundle is a basic extension to the geometric domain of the fundamental idea of a vector space. Given a space X, we take a real or complex finite dimensional vector space V and. U. Koschorke Vector Fields and Other Vector Bundles Morphisms—A Singularity Approach Lecture Notes in Math.,Springer, Berlin ().

Operations on Vector Bundles.- 5. Splitting of Vector Bundles.- IV Vector Fields and Differential Equations.- 1. Existence Theorem for Differential Equations.- 2. Vector Fields, Curves, and Flows.- 3. Sprays.- 4. The Flow of a Spray and the Exponential Map.- 5. Existence of Tubular Neighborhoods.- 6.

Uniqueness of Tubular Neighborhoods.- V. ﬁber of the vector bundle. Vector bundles thus combine topology with linear algebra, and the study of vector bundles could be called Linear Algebraic Topology.

The only two vector bundles with base space a circle and one-dimensional ﬁber are the M¨obius band and the annulus, but the classiﬁcation of all the d iﬀerent vector.Vector bundle morphisms are a special case of the notion of a bundle map between fiber bundles, and are also often called (vector) bundle homomorphisms.In mathematics—more specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle and the cotangent bundle ∗ of a pseudo-Riemannian manifold induced by its metric are similar isomorphisms on symplectic term musical refers to the use of the symbols ♭ (flat) and ♯ (sharp).