New York Journal of Mathematics
Volume 21 (2015) 943-953

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Piotr Bartłomiejczyk and Piotr Nowak-Przygodzki

The Hopf theorem for gradient local vector fields on manifolds

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Published: September 21, 2015
Keywords: Gradient vector field, otopy, equivariant map
Subject: Primary: 55Q05; secondary: 55M25
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.
Acknowledgements

The second author was partially supported by Polish Research Grant NCN 2011/03/B/ST1/04533.
Author information

Piotr Bartłomiejczyk:
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
pbartlomiejczyk@mif.pg.gda.pl

Piotr Nowak-Przygodzki:
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
piotrnp@wp.pl