The Hopf theorem for gradient local vector fields on manifolds

Piotr Bartłomiejczyk; Piotr Nowak-Przygodzki

The Hopf theorem for gradient local vector fields on manifolds

Abstract

We prove the Hopf theorem for gradient local vector fields on manifolds, i.e., we show that there is a natural bijection between the set of gradient otopy classes of gradient local vector fields and the integers if the manifold is connected Riemannian without boundary.

Authors (2)

Piotr Bartłomiejczyk dr hab.
Piotr Nowak-Przygodzki
- WFTiMS PG KRRiZM

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Keywords

GRADIENT VECTOR FIELD, OTOPY, EQUIVARIANT MAP.

Details

Category:: Articles
Type:: artykuł w czasopiśmie wyróżnionym w JCR
Published in:: New York Journal of Mathematics no. 21, pages 943 - 953,
ISSN: 1076-9803
Language:: English
Publication year:: 2015
Bibliographic description:: Bartłomiejczyk P., Nowak-Przygodzki P.: The Hopf theorem for gradient local vector fields on manifolds// New York Journal of Mathematics. -Vol. 21, (2015), s.943-953
Verified by:: Gdańsk University of Technology