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100%: Michael Francis Atiyah: Vector Fields on Manifolds (ISBN: 9783322985033) 2013, in Englisch, Taschenbuch.Nur diese Ausgabe anzeigen…
100%: Michael Francis Atiyah: Vector Fields on Manifolds (ISBN: 9783322979414) 1970, in Englisch, Taschenbuch.Nur diese Ausgabe anzeigen…
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1
Vector Fields on Manifolds
~EN PB NWISBN: 9783322979414 bzw. 3322979415, vermutlich in Englisch, Springer Shop, Taschenbuch, neu.
Lieferung aus: Vereinigte Staaten von Amerika, Lagernd, zzgl. Versandkosten.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). Soft cover.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). Soft cover.
2
Vector Fields on Manifolds
~EN NW EB DLISBN: 9783322985033 bzw. 3322985032, vermutlich in Englisch, Springer Shop, neu, E-Book, elektronischer Download.
Lieferung aus: Vereinigte Staaten von Amerika, Lagernd, zzgl. Versandkosten.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). eBook.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). eBook.
3
Vector Fields on Manifolds
~EN NW EB DLISBN: 9783322985033 bzw. 3322985032, vermutlich in Englisch, VS Verlag Fur Sozialwissenschaften, neu, E-Book, elektronischer Download.
Lieferung aus: Deutschland, Versandkostenfrei.
Vector Fields on Manifolds: This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist- ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens- ions of Hopf`s theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). Englisch, Ebook.
Vector Fields on Manifolds: This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist- ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens- ions of Hopf`s theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). Englisch, Ebook.
4
Vector Fields on Manifolds (Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen) (2013)
EN NW EB DLISBN: 9783322985033 bzw. 3322985032, in Englisch, 28 Seiten, VS Verlag für Sozialwissenschaften, neu, E-Book, elektronischer Download.
Lieferung aus: Deutschland, E-Book zum Download, Versandkostenfrei.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). Kindle Edition, Format: Kindle eBook, Label: VS Verlag für Sozialwissenschaften, VS Verlag für Sozialwissenschaften, Produktgruppe: eBooks, Publiziert: 2013-03-09, Freigegeben: 2013-03-09, Studio: VS Verlag für Sozialwissenschaften.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts that the vanishing of the Euler characteristic is the necessary and sufficient condition, and our results will give partial extens ions of Hopf's theorem to the case r > 1. Arecent article by E. Thomas [10] gives a good survey of work in this general area. Our approach to these problems is based on the index theory of elliptic differential operators and is therefore rather different from the standard topological approach. Briefly speaking, what we do is to observe that certain invariants of a manifold (Euler characteristic, signature, etc. ) are indices of elliptic operators (see [5]) and the existence of a certain number of vector fields implies certain symmetry conditions for these operators and hence corresponding results for their indices. In this way we obtain certain necessary conditions for the existence of vector fields and, more generally , for the existence of fields of tangent planes. For example, one of our results is the following THEOREM (1. 1). Let X be a compact oriented smooth manifold 0/ dimension 4 q, and assume that X possesses a tangent fteld of oriented 2-planes (that is, an oriented 2-dimensional sub-bundle 0/ the tangent vector bundle). Kindle Edition, Format: Kindle eBook, Label: VS Verlag für Sozialwissenschaften, VS Verlag für Sozialwissenschaften, Produktgruppe: eBooks, Publiziert: 2013-03-09, Freigegeben: 2013-03-09, Studio: VS Verlag für Sozialwissenschaften.
5
Vector Fields on Manifolds (2013)
EN NW EB DLISBN: 9783322985033 bzw. 3322985032, in Englisch, VS Verlag für Sozialwissenschaften, VS Verlag für Sozialwissenschaften, VS Verlag für Sozialwissenschaften, neu, E-Book, elektronischer Download.
Lieferung aus: Vereinigtes Königreich Großbritannien und Nordirland, in-stock.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist- ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts th.
This paper is a contribution to the topological study of vector fields on manifolds. In particular we shall be concerned with the problems of exist- ence of r linearly independent vector fields. For r = 1 the classical result of H. Hopf asserts th.
8
Vector Fields on Manifolds (1970)
~EN PB NWISBN: 9783322979414 bzw. 3322979415, vermutlich in Englisch, Teubner, Leipzig, Deutschland, Taschenbuch, neu.
Lieferung aus: Deutschland, Next Day, Versandkostenfrei.
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