A Condition for a Closed One-Form to Be Exact

A condition for a closed one-form to be exact, the one-form having values in Euclidean space, on a compact surface without boundary, is given in the case where the surface has suitable differentiable automorphisms. Tori and hyperelliptic curves, with holomorphic automorphisms, are in this case. A lo...

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Bibliographic Details
Published in:	Advances in applied Clifford algebras Vol. 22; no. 2; pp. 433 - 448
Main Author:	Moriya, Katsuhiro
Format:	Journal Article
Language:	English
Published:	Basel SP Birkhäuser Verlag Basel 01-06-2012
Subjects:	Applications of Mathematics Mathematical and Computational Physics Mathematical Methods in Physics Physics Physics and Astronomy Theoretical period closed one-form differentiable automorphism Exact one-form
Online Access:	Get full text
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Summary:	A condition for a closed one-form to be exact, the one-form having values in Euclidean space, on a compact surface without boundary, is given in the case where the surface has suitable differentiable automorphisms. Tori and hyperelliptic curves, with holomorphic automorphisms, are in this case. A local representation formula for surfaces in Euclidean space is then globalized. A condition for a local surface of constant mean curvature to be global, can be written using a harmonic Gauss map.
ISSN:	0188-7009 1661-4909
DOI:	10.1007/s00006-011-0313-5