Abstract
The index of a meromorphic function g on a compact Riemann surface is an invariant of g, which is defined as the number of negative eigenvalues of the differential operator L:=—Δ—| dG |2, where Δ is the Laplacian with respect to a conformal metric ds2 on the Riemann surface and G:M→S2 is the holomorphic map corresponding to g. We consider the meromorphic function w on the Riemann surface Ma={(z,w)∈ℂ^2|w2=z(z−a)(z+1a)}(a≥1) homeomorphic to a torus. We find a0>1 and determine the index of tw for all a in the range 1≤a≤a0 and all t>0.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
